Practice: If the force between two charges is F when the distance is d, what will the force between the two charges be if they were moved to a distance of 2d

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Practice: If the force between two charges is F when the distance is d, what will the force between the two charges be if they were moved to a distance of 2d

Practice: In which direction will the – 1 C charge move? If it has a mass of 10 g, what will its initial acceleration be?

Practice: What is the direction of the net force on the charge at the center of the square in the following figure?

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Concept #1: Coulomb's Law

Practice #1: Changing Distance (Proportional Reasoning)

Example #1: Charges In A Line (Find Zero Force)

Practice #2: Three Charges In Line

Example #2: Charges In A Triangle (Rank Force Pairs)

Example #3: Charges in a Plane

Example #4: Exploiting Symmetry

Practice #3: Direction of Net Force On Square

Example #5: Electroscope (Find Charge)

A point charge Q = -12 μC, and two other charges, q 1 and q2, are placed as shown. The electric force components on charge Q are Fx = +0.005 N and Fy = -0.003 N. Find charge q1 and q2.

Two small beads having charges q1 = +9Q and q2 = -Q are fixed on a horizontal insulating rod. The distance between q1 and q2 is d = 1.5 m The third bead with charge q 3 = +Q is at the right hand side of the second bead and is free to slide along the axis of the rod. At what position x is the third bead in equilibrium?

Two charges q1 and q2 are separated by a distance d and exert a force F on each other. What is the new force F ′ , if charge 1 is increased to q ′1 = 5 q1, charge 2 is decreased to q ′2 = q2 / 2, and the distance is decreased to d ′ = d / 2? Choose one.
1. F ′ = 5/2 F
2. F ′ = 5/4 F
3. F ′ = 20 F
4. F ′ = 25/4 F
5. F ′ = 50 F
6. F ′ = 25/2 F
7. F ′ = 100 F
8. F ′ = 5 F
9. F ′ = 25 F
10. F ' = 10 F

Two charges, Q1 and Q2, are separated by a certain distance R. If the magnitudes of their charges are doubled and their separation is halved, then what happens to the electrical force between these charges?
A) It increases by a factor of 16.
B) It is quadrupled.
C) It is doubled.
D) It stays the same.

Two point charges of +60.0 μC and -12.0 μC are separated by a distance of 20.0 cm. A +7.00 μC charge is placed midway between these two charges. What is the electric force acting on this charge because of the other two charges?
A) 4.53 N directed towards the positive charge
B) 453 N directed towards the negative charge
C) 4.53 N directed towards the negative charge
D) 453 N directed towards the positive charge

Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude F due to the other. With time, charge gradually leaks off of both spheres. When each of the spheres has lost half its initial charge, the magnitude of the electrostatic force will be
(a) 1/2 F
(b) 1/16 F
(c) 1/8 F
(d) 1/4 F

A positive charge Q is fixed on a very large horizontal frictionless tabletop. A second positive point charge q is released from rest near the stationary charge and is free to move. Which statement best describes the motion of q after it is released?
(a) As it moves farther and farther from Q, its acceleration will keep increasing.
(b) As it moves farther and farther from Q, its speed will decrease.
(c) Its speed will be greatest just after it is released.
(d) Its acceleration is zero just after it is released.
(e) As it moves farther and farther from Q, its speed will keep increasing.

A positive test charge q is released near a positive fixed charge Q. As q moves away from Q, it will move with
A) increasing acceleration.
B) constant velocity.
C) decreasing acceleration.
D) constant acceleration.

Three charges, q1, q2 and q3 are placed left to rigth in a straight line. The distance between q1 and q2 is twice the distance between q 2 and q3. Charge q1 is negative. If the force on charge q3 is zero, which of the following statements about q 2 is true?
A) q2 is negative with a magnitude twice that of q 1
B) q2 is negative with a magnitude half that of q 1
C) q2 is positive with a magnitude one fourth that of q 1
D) q2 is positive with a magnitude one ninth that of q 1
E) q2 is positive with a magnitude equal that of q 1

Three identical point charges, Q = 3μC, are placed at the vertices of an equilateral triangle as shown in the figure. The length of each side of the triangle is d = 0.15m. Determine the magnitude and direction of the total electrostatic force on the charge at the top of the triangle.

At what separation will two charges, each of magnitude 6.0 μC, exert a force of 0.70 N on each other?
A) 1.1 x 10-5 m
B) 0.23 m
C) 0.48 m
D) 0.68 m
E) 1.4 m

Find the magnitude and direction of the net electrostatic force on q 1 due to q 2 and q3 as shown in the figure. The charges are q 1 = +4.0 μC, q2 = -6.0 μC, q3 = -5.0 μC.

Five charges are equally spaced along the x axis. Each charge has the same magnitude e, but some of the charges are +e and some are −e. Four different configurations of charge are labelled A, B, C, D in the figure. Rank the magnitude of the force on the middle charge for the different configurations with largest first and smallest last.
(1) C,D,A,B
(2) C,A,D,B
(3) D,C,A,B
(4) A,C,D,B
(5) C,B,D,A

An oil droplet with 4 excess electrons is held stationary in a field of 1.27x10 4 N/C. What is the radius of the oil drop? (The density of the oil is 824 kg/m3, e = 1.60 x 10 -19 C.)

Three charges are placed at the following (x, y) coordinates: charge + 6.0x10 -6 C at (0, 0.5 m), charge + 2.0x10 -6 C at (0.7, 0 m), and charge - 4.0 x 10 -6 C at (0.7 m, 0.5 m). Calculate the electrical force on a point particle with charge -1.6 x 10-6 C at the origin (0,0).

What is the difference between the electric force on a charge q when moved from a distance d to a distance 3d. Consider the initial electric force to be F0.

Two identical, 0.25 μC charges hang from the end of electroscope leaves. If, in equilibrium, the electroscope leaves deflect from one another to an angle of 40° from the horizontal axis, as shown in the figure, what is the mass of each charge?

A dipole with negative charge of -5.0 x 10 -6 C on the x-axis at x = -3.0 cm, and a positive charge of 5.0 x 10-6 C on the x-axis at x = + 3.0 cm. A negative point charge of q = -4.0 x 10-6 C is placed on the y-axis at y = -4.0 cm.
a) Draw the two forces acted on the negative point charge q = -4.0 x 10 -6 C (in arbitrary scale, but correct DIRECTION).
b) How big is the TOTAL eletrostatic force acted on the -4.0 x 10 -6 C charge? What is its direction? (i.e., the angle with respect to the x-direction).

A positive test charge q is released near a positive fixed charge Q. As q moves away from Q, it will move with
A) constant velocity.
B) constant acceleration.
C) decreasing acceleration.
D) increasing acceleration.

Two equally charged spheres of mass 1.0 g are placed 2.0 cm apart. When released, they begin to accelerate at 779 m/s2. What is the magnitude of the charge on each sphere?
A) 160 nC
B) 130 nC
C) 190 nC
D) 100 nC

What is the magnitude of an electric field that balances the weight of a plastic sphere of mass 2.2 g that has been charged to -3.0 nC?
A) 7.2x106 N/C
B) 8.1x105 N/C
C) 1.5x106 N/C
D) 2.2x106 N/C

Two charged particles of equal magnitude (−Q and +Q) are fixed at opposite corners of a square that lies in a plane (see figure below). A test charge +q is placed at a third corner. What is the direction of the force on the test charge due to the two other charges?

Two charged particles of equal magnitude (−Q and +Q) are fixed at opposite corners of a square that lies in a plane (see figure below). A test charge +q is placed at a third corner. What is the direction of the force on the test charge due to the two other charges?If F is the magnitude of the force on the test charge due to only one of the other charges, what is the magnitude of the net force acting on the test charge due to both of these charges?

Two positive point charges Q and 2Q are separated by a distance R. If the charge Q experiences a force of magnitude F when the separation is R, what is the magnitude of the force on the charge 2Q when the separation is 2R?
A) F/4
B) F/2
C) F
D) 2F
E) 4F

An equilateral triangle ABC. A positive point charge +q is located at each of the three vertices A, B, and C. Each side of the triangle is of length a. A point charge Q (that may be positive or negative) is placed at the mid-point between B and C. Is it possible to choose the value of Q (that is non-zero) such that the force on Q is zero?
A) Yes, because the forces on Q are vectors and three vectors can add to zero.
B) No, because the forces on Q are vectors and three vectors can never add to zero.
C) Yes, because the electric force at the mid-point between B and C is zero whether a charge is placed there or not.
D) No, because the forces on Q due to the charges at B and C point in the same direction.
E) No, because a fourth charge would be needed to cancel the force on Q due to the charge at A.

Electrical and gravitational forces follow similar equations with one main difference:
A) Gravitational forces obey the inverse square law and electrical forces do not.
B) Electrical forces obey the inverse square law and gravitational forces do not.
C) Gravitational forces are always attractive but electrical forces can be attractive or repulsive.
D) Electrical forces attract and gravitational forces repel.

The force of attraction between a -40.0 μC and +108 μC charge is 4.00 N. What is the separation between these two charges?A) 1.13 mB) 3.67 mC) 3.12 mD) 2.49 m

Four charges are arranged as shown in the figure below each with a positive (red) charge or a negative (blue) charge. Find the net total force (magnitude and direction) exerted on the charge with + 6.0 micro coulomb by the other three charges.

Three point charges +3 μC, +4 μC, and -7 μC are placed along the x and y axis with the values and positions shown. What is the net force, magnitude and direction, acting on the +4 μC charge?
(a) 198 N, 37° above +x axis
(b) 298 N, 47° above -x axis
(c) 342 N, 53° above +x axis
(d) 305 N, 53° below +x axis

Two identical small charged spheres hang in equilibrium with equal masses as shown in the figure. The length of the strings are equal and the angle (shown in the figure) with the vertical is identical.The acceleration of gravity is 9.8 m/s 2 and the value of Coulomb’s constant is 8.98755×10 9 N m2/C2.

Four charges −5×10−9 C at (0m, 0m), −8×10−9 C at (1m, 5m), 9×10−9 C at (3m, 1m), and 7×10−9 C at (3m, −3m), are arranged in the ( x, y ) plane (as shown in the figure below, where the scale is in meters).Find the magnitude of the resulting force on the −5 nC charge at the origin [coordinates, (0m, 0m)].

Two identical spheres A and B carry charges Q and 2Q, respectively. They are separated by a distance much larger than their diameters. A third identical conducting sphere C is uncharged. Sphere C is first touched to A, then to B, and finally removed. As a result, the electrostatic force between A and B, which was originally F, becomes:
(1) 5F/16
(2) F/4
(3) 3F/8
(4) F/8
(5) 7F/16

A charge q1 = -18.0 nC hangs from a string. It has a mass of 2.9 g. A second charge of q2 = 53.7 nC is brought to a distance of 2.3 cm from q 1. Find the angle θ assuming the system is at rest as shown in the figure.
A. 15°
B. 21.3°
C. 30°
D. 45°
E. 47.3°

Three charges are positioned as indicated in the figure. What are the horizontal and vertical components of the net force exerted on the +15 µC charge by the +11 µC and + µC charges?

An alpha particle with charge +2.0 e is sent at high speed toward a silver nucleus with charge +47e. What is the electric force acting on the alpha particle when the alpha particle is 4.2 × 10−14 m from the silver nucleus? The value of the Coulomb constant is 8.99 × 10 9 N·m2/C2.1. Unable to determine2. 12.2639 N, repulsive3. 13.0467 N, repulsive4. 12.2639 N, attractive5. 13.0467 N, attractive6. None of these

What is the net electric force on the 1 C charge? Consider the 1 C to placed directly in the center of the arrangement.

What is the force F? on the 1.0 nC charge in (Figure 1)?A) Determine the magnitude of the force.B) Determine the direction of the force.

The force of attraction between a -40.0 μC and + 108 μC charge is 4.00 N. What is the separation between these two charges?A) 1.13 m B) 2.10 m C) 3.12 m D) 2.49 m E) 3.67 m

Two identical metal balls are suspended by insulating threads. Both balls have the same net charge. In this problem, do not assume the balls are point charges a. Draw a separate free-body diagram for each ball. Label the forces to indicate:the object exerting the force,the object on which the force is exerted, the type of force (gravitational, normal, etc.), and whether the force is a contact or a non-contact force.b. Suppose the charge on the second ball is reduced slightly, so that it is less than that on the first ball.Predict whether the angle as that ball 1 makes with the vertical will be greater than, less than or equal to the angle that ball 2 makes with the vertical. Explain. Sketch your answer above.How does the free-body diagram for each ball in this case compare to the corresponding free body diagram that you drew in part a? If the magnitudes or directions of any of the forces change, describe how they change.c. Predict what will happen if the net charge on ball 2 is reduced to zero. Make a sketch to illustrate your answer.

A. What is the magnitude of the electric force on charge A in the figure?F=______NB. What is the direction of the electric force on charge A in the figure? Choose the best answer.(a) to the left(b) to the right(c) the force is zero

Two small aluminum spheres, each of mass 0.0250 kilograms, are separated by 80.0 centimeters.a. How many electrons does each sphere contain? (The atomic mass of aluminum is 26.982 grams per mole, and its atomic number is 13.)b. How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude 1.00 × 104 N( roughly one ton)? Assume that the spheres may be treated as point charges.c. What fraction of all the electrons in one of the spheres does this represent?

Part AWhat is the strength of an electric field that will balance the weight of a proton?Part BWhat is the direction of an electric field that will balance the weight of a proton?a) upwardb) downwardPart C What is the strength of an electric field that will balance the weight of an electron?Part DWhat is the direction of an electric field that will balance the weight of an electron?a) upwardb) downward

An electron and a proton are each moving at 795 km/s in perpendicular paths as shown in (Figure 1) .Part AFind the magnitude of the total electrical force that the electron exerts on the proton.Part BFind the direction of the total electrical force that the electron exerts on the proton

At what distance is the electrostatic force between two electrons equal to the weight of one?

The net force on the 1.0 nC in the figure charge is zero. What is q?

Two charged particles, with charges q1 = q and q2 = 4q, are located at a distance d = 2.00cm apart on the x-axis. A third charged particle, with charge q3 = q, is placed on the x-axis such that the magnitude of the force that charge 1 exerts on charge 3 is equal to the force that charge 2 exerts on charge 3. Find the position of charge 3 when q = 2.00 nC. Assuming charge 1 is located at the origin of the x-axis and the positive x-axis points to the right, find the two possible values, x3,r and x3,l for the position of charge 3.

Three point charges are arranged on a line:Charge q3 = +5.00×10-9 C and is at the origin.Charge q2 = −3.00×10-9 C and is at x = +4.00cm. Charge q1 is at x=+2.00cm.What is the magnitude and sign (+ or −) for q1 if the net force on q3 is zero?

A 2.4 nC charge is at the origin and a -4.8 nC charge is at x = 1.1 cm .Part AAt what x -coordinate could you place a proton so that it would experience no net force?Part BWould the net force be zero for an electron placed at the same position?NoYes

(a) In Figure 18.59, four equal charges q lie on the corners of a square. A fifth charge Q is on a mass m directly above the center of the square, at a height equal to the length d of one side of the square. Determine the magnitude of q in terms of Q , m , and d , if the Coulomb force is to equal the weight of m. (b) Is this equilibrium stable or unstable? Discuss.

A point charge +3 q is located at the origin and a point charge -q is located on the x-axis at d = 0.5 m. At what location on the x-axis will a third charge q0 experience no net force from the other two charge?

Four equal positive point charges, each of charge 5.7 µC , are at the corners of a square of side 9.2 cm. What charge should be placed at the center of the square so that all charges are at equilibrium?

Two 4.0 kg masses are 2.0 m apart on a frictionless table. Each has 1.0 μC of charge. What is the magnitude of the electric force on one of the masses? What is the initial acceleration of each mass if they are released and allowed to move?

At what distance is the electrostatic force between two protons equal to the weight of one proton?

Two charges are placed on the x-axis: one of 2.5 μC at the origin and the other of -3.5μC at x =0.6 m. Find the position on the x-axis where the net force on a small charge +q would be zero

What is the repulsive force between two pith balls that are 8 cm apart and have equal charges of -30 nC?

A charge +Q is located at the origin and a second charge, + 4Q, is at distance d on the X-axis.A. Where should a third charge,q , be placed, so that all three charges will be in equilibrium? Express your answer in terms of d .B. What should be its sign, so that all three charges will be in equilibrium? Negative or Positive?C. What should be its magnitude, so that all three charges will be in equilibrium? Express your answer in terms of Q .

Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude F due to the other. With time, charge gradually diminishes on both spheres by leaking off. When each of the spheres has lost half its initial charge, what will be the magnitude of the electrostatic force on each one?A) 1/16 FB) 1/8 FC) 1/4 FD) 1/2 FE) 1/√2 F

The figure shows four charges at the corners of a square of side L. Assume q and Q are positive.What is the magnitude of the net force on q?Give your answer in terms of Q, q, L and constant K.

In the diagram below, there are three collinear point charges: q1, q2, and q3. The distance between q1 and q2 is the same as that between q2 and q3Rank the six combinations of electric charges on the basis of the electric force acting on q1. Define forces pointing to the right as positive and forces pointing to the left as negative. Rank positive forces as larger than negative forces. Rank from largest to smallest, placing the largest on the left and the smallest on the right.

Four equal positive point charges q are fixed to the corners of a horizontal square. A fifth positive point charge Q is on a free particle of mass m positioned directly above the center of the square, at a height equal to the length d of one side of the square. Refer to the figure. Determine the magnitude of q in terms of defined quantities, the Coulomb constant, and g, if the system is in equilibrium.

Two charged balls, one with a charge of +5.0 μC and the other with a charge of +2.4 μC, are placed a distance d = 10.0 cm apart from each other and rigidly held in place. A third ball with a charge of -3.0 μC is dangled from a string between the two charged balls such that it remains in equilibrium. Calculate the distance the third charged ball is from to the +2.4 μC charge.

Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius α and positive charge q distributed evenly along its circumference.1. What is the magnitude of the electric field along the positive z axis?Use k in your answer, where . ( E(z)=? )

Three point charges are arranged as shown in Figure. (a) Find the vector electric field that the q = 7.50 nC and -3.00 nC charges together create at the origin. N/C + N/C (b) Find the vector force on the 5.00 nC charge.

There is a force between two charged objects. To decrease the magnitude of the force, we can: A. Move the objects farther from each other or increase the charge on either of them. B. Move the objects farther from each other or reduce the charge on either of them. C. Move the objects closer to each other or increase the charge on either of them. D. Move the objects closer to each other or reduce the charge on either of them.

The magnitude of the electric force between two protons is 2.3 x 10-26 N. How far apart are they?a) 1b) 0.10 mc) 0.0057 m d) 0.48 me) 0.022 mf) 3.1 m

In the late 19th century, great interest was directed toward the study of electrical discharges in gases and the nature of so-called cathode rays. One remarkable series of experiments with cathode rays, conducted by J. J. Thomson around 1897, led to the discovery of the electron.With the idea that cathode rays were charged particles, Thomson used a cathode-ray tube to measure the ratio of charge to mass, q/m, of these particles, repeating the measurements with different cathode materials and different residual gases in the tube.What is the distance Δy between the two points that you observe? Assume that the plates have length d, and use e and m for the charge and the mass of the electrons, respectively.Express your answer in terms of e, m, d, v0, L, and E0.

A charge 5.02 nC is placed at the origin of an xy-coordinate system, and a charge -2.05 nC is placed on the positive x-axis at x = 4.00cm. A third particle, of charge 6.03 nC is now placed at the point x = 4.00 cm , y = 3.02 cm .1. Find the x-component of the total force exerted on the third charge by the other two.2. Find the y-component of the total force exerted on the third charge by the other two.3. Find the magnitude of the total force acting on the third charge.4. Find the direction of the total force acting on the third charge. ( radians between F? and +x-axis )

Two small spheres spaced 20.0 cm apart have equal charge.How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 4.57 x 10-21 N?Number of Electrons = ?

Three point charges are arranged along the x-axis. Charge q1 = 3 mc is at the origin and charge q2 = -5 mc is at x = 0.2 m. Charge q3 = -8.00 mc.Where is q3 located if the net force on q1 is 7.00 N in the -x-direction?

In the figure, the point charges are located at the corners of an equilateral triangle 22 cm on a side.A.)What is the magnitude of the force in N on Qa given that Qa = 1.3nC?B.)What is the direction of the force on Qa in degrees above the negative x-axis with origin at Qa?

As shown in the figure, there are 3 point charges along the x-axis located at 3, 8, and 11 cm.What is the x-component of the force on the charge located at x = 8 cm given that q = 0.85 uC in N? Fx = ?

(Figure 1) shows four charges at the corners of a square side L.What magnitude and sign of charge Q will make the force on charge q zero?

An atomic nucleus has a charge of +40e. An electron is 10-9 m from the nucleus. What is the force on the electron?A) 2.9 nN B) 9.2 nNC) 3.7 nN D) 1000 C E) 6.8 nN

What is the magnitude of the force F on the 5.0 nC charge in the figure? What is the direction of the force F on the 5.0 nC charge in the figure?

Free charges do not remain stationary when close together. To illustrate this, calculate the magnitude of the instantaneous acceleration, in meters per second squared, of two isolated protons separated by 2.5 nm.

A 2.6 mm -diameter sphere is charged to -4.6 nC . An electron fired directly at the sphere from far away comes to within 0.37 mm of the surface of the target before being reflected. What is the acceleration of the electron at its turning point?

Consider three plastic balls (A, B, and C), each carrying a uniformly distributed charge equal to either +Q, -Q or zero, and an uncharged (neutral) copper ball (D). A positive test charge (T) experiences the forces shown in the figure when brought very near to the individual balls. The test charge T is strongly attracted to A, strongly repelled from B, weakly attracted to C, and strongly attracted to D.What is the nature of the force between balls A and B?a) strongly attractiveb) strongly repulsivec) weakly attractived) neither attractive nor repulsive

The dipole moment of the water molecule (H2O)is 6.17×10−30 C⋅m. Consider a water molecule located at the origin whose dipole moment p points in the positive x direction. A chlorine ion (Cl−), of charge −1.60×10−19C, is located at x=3.00×10−9 meters. Assume that this x value is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis can be used.Find the magnitude of the electric force, ignoring the sign, that the water molecule exerts on the chlorine ion.

Two point charges, with charges q1 and q2, are each moving with speed v toward the origin. At the instant shown q1 is at position (0, d) and q2 is at (d, 0). (Note that the signs of the charges are not given because forces between the charges.) Part A. What is the magnitude of the electric force between the two charges? Express F in terms of q, d and ε0Part B. What is the magnitude of the magnetic force on q2 due to the magnetic field caused by q1? Express the magnitude of the magnetic force in terms of q, v, d and μ0Part. C Assuming that the charges are moving nonrelativistically (u < c), what can you say about the relationship between the magnitudes of the magnetic and electrostatic forces? a. The magnitude of the magnetic force is greater than the magnitude of the electric force. b. The magnitude of the electric force is greater than the magnitude of the magnetic force. c. Both forces have the same magnitude.

What is the magnitude of the force F on the 1.0 nC charge in the figure?

Two tiny beads are 25 cm apart with no other charges or fields present. Bead A carries 10 μC of charge and bead B carries 1 μC. Which one of the following statements is true about the magnitudes of the electric forces on these beads? A) The force on A is 10 times the force on B. B) The force on B is 10 times the force on A. C) The force on A is exactly equal to the force on B. D) The force on A is 100 times the force on B. E) The force on B is 100 times the force on A.

A point charge with charge q1 is held stationary at the origin. A second point charge with charge q2 moves from the point (x1, 0) to the point (x2, y2).How much work W is done by the electrostatic force on the moving point charge? Express your answer in joules. Use k for Coulomb's constant.

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