Practice: A 1.5uC charge, with a mass of 50g, is in the presence of an electric field that perfectly balances its gravity. What magnitude does the electric field need to be, and in what direction does it need to point?

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Practice: A 1.5uC charge, with a mass of 50g, is in the presence of an electric field that perfectly balances its gravity. What magnitude does the electric field need to be, and in what direction does it need to point?

Practice: If two equal charges are separated by some distance, they form an electric dipole. Find the electric field at the center of an electric dipole, given by the point P in the following figure, formed by a 1C and a – 1C charge separated by 1 cm.

Practice: 4 charges are arranged as shown in the following figure. Find the electric field at the center of the arrangement, indicated by the point P.

Practice: In the following figure, a mass m is balanced such that its tether is perfectly horizontal. If the mass is m and the angle of the electric field is 𝜃, what is the magnitude of the electric field, E?

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Concept #1: Intro to Electric Fields

Practice #1: Balancing Gravity

Concept #2: Electric Field due to a Point Charge

Example #1: Zero Electric Field due to Two Charges

Practice #2: Electric Field at Center of Dipole

Example #2: Electric Field Above Two Charges (Triangle)

Practice #3: Electric Field at Center of Four Charges

Example #3: Balancing a Pendulum in Electric Field

Practice #4: Balance Mass in Electric Field (Angled)

An electron traveling along the +x-axis enters an electric field that is directed vertically down, i.e., along the negative y-axis. What will be the direction of the electric force acting on the electron after entering the electric field?
A) -y
B) +y
C) +x
D) -x

A charged particle traveling along the +x axis enters an electric field directed vertically upward along the +y axis. If the charged particle experiences a force downward because of this field, what is the sign of the charge on this particle?
A) It is neutral.
B) It is positive.
C) It is negative.
D) None of previous is correct.

Two charged particles are located at x = -a and x = +a, as shown below, on the x-axis. The electric field produced by these two charges at any point on the y-axis, is always
A) in the +y direction
B) in the -y direction
C) in the +x direction
D) in the -x direction

Two charges, q1 = -2.50 nC and q 2 = +2.00 nC, are placed 0.400 m apart as shown in the figure. What is the magnitude of the electric field at point P, 0.300 m above q 2?
A) 71.9 N/C
B) 218 N/C
C) 53.9 N/C
D) 163 N/C
E) 146 N/C

Two charges, q1 = -2.50 nC and q 2 = +2.00 nC, are placed 0.400 m apart as shown in the figure. What is the direction of the electric field at point P, 0.300 m above q 2?
A) 116° counter-clockwise from the positive x-axis.
B) 63.7° clockwise from the positive x-axis.
C) 72.4° counter-clockwise from the positive x-axis.
D) 108° clockwise from the positive x-axis.
E) 90° counter-clockwise from the positive x-axis.

Two charges, q1 = 5 μC and q 2 = 7 μC, are separated by 10 cm, with q 1 to the left of q2. Where is the net electric field, due to both charges, zero?

A pendulum has a charged mass at the end of it, as shown in the figure below. If it is in equilibrium, what is the magnitude of the electric field?

Find the electric field at point P due to the charges shown.

Two charged metal plates in vacuum are 0.15 m apart, with an electric field between the plates of E = 3000 N/C. A proton (q= +e = 1.6x10-19 C, m = 1.67x10 -27 kg) is shot with a speed of 2x105 m/s from the positive plate. What will be its speed before hitting the negative plate?

Two point charges having charge of -6.25 x 10 -9 C and -12.5 x 10 -9 are 25.0 cm apart.
a) Calculate the magnitude of Coulomb force between them. Is it repulsive or attractive?
b) What is the magnitude of electric field at point A? What is its direction?

A charge of 3 μC is at the origin. The Coulomb constant is 8.98755 × 10 9 Nm2/C2. What is the magnitude of the electric field on the x axis at x = −5 m?

Four identical point charges, q, are placed at the corners of a square. Each side of the square has length L. What is the magnitude of the electric field at the point P, the center of the square?
A) 0
B) kq2/L2
C) kq2/2L2
D) kq2/4L2

In the figure, point B is a distance L away from a point charge Q. Point A is a distance 4L away from Q. What is the ratio of the electric field at A to that at B, EA/EB?
A) 1/16
B) 1/9
C) 1/4
D) 1/3
E) This cannot be determined

The four charges form a square of edge length a. What is the direction of the net electric field at the square's center?
a. -x
b. +x
c. +y
d. -y
e. The field is zero at the center.

An electron traveling horizontally at 6 × 10 6 m/s enters a 0.05 m region with a uniform electric field of 89 N/C , perpendicular to the electron's velocity. The mass of an electron is 9.10939 × 10−31 kg and the charge on an electron is 1.60218 × 10−19 C . What is the magnitude of the vertical displacement ∆y of the electron while it is in the electric field?
1. 0.00485434
2. 0.000543524
3. 0.0148796
4. 0.0649004
5. 0.00403356
6. 0.000873782
7. 0.00354891
8. 0.0176498
9. 0.00427393
10. 0.00586273

The figure shows two unequal point charges, q and Q, of opposite sign. Charge Q has greater magnitude than charge q. In which of the regions X, Y, Z will there be a point at which the net electric field due to these two charges is zero?(a) only region X(b) only regions X and Z(c) only region Y(d) only region Z(e) all three regions

Two point charges are separated by 20 cm and have charges of +8.0 and +16.0 μC, respectively. What is the electric field at a point midway between the two charges?
(a) 28.8 x 106 N/C
(b) 1.44 x 107 N/C
(c) 7.2 x 106 N/C
(d) zero+

Three point charges are placed at the vertices of an equilateral triangle. Find the magnitude of the electric field E at P. The value of the Coulomb constant is 8.9875 × 109 N · m2/C2. Answer in units of N/C.

An electron is accelerated by a constant electric field of magnitude 208 N/C.
A) Find the magnitude of the acceleration of the electron. The mass of an electron is 9.109 × 10−31 kg and the elemental charge is 1.6 × 10−19 C. Answer in units of m/s2.
B) Find the electron’s speed after 1.93 × 10−8 s, assuming it starts from rest. Answer in units of m/s.

An electron traveling at 2 × 106 m/s enters a 0.08 m region with a uniform electric field of 246 N/C , as in the figure.
A) Find the magnitude of the acceleration of the electron while in the electric field. The mass of an electron is 9.109 × 10−31 kg and the fundamental charge is 1.602 × 10−19 C . Answer in units of m/s2.
B) Find the time it takes the electron to travel through the region of the electric field, assuming it doesn’t hit the side walls. Answer in units of s.
C) What is the magnitude of the vertical displacement ∆y of the electron while it is in the electric field? Answer in units of m.

Two unequal point charges are separated as shown in the figure. The electric field due to this combination of charges can be zero.
a) Only in region 1.
b) Only in region 2.
c) Only in region 3.
d) In both regions 1 and 3.

In the four configurations of charges, all the charges are the same magniture, Q, but can be positive or negative. The distance between adjacent items is always the same. In which situation is the magnitude of the electric field at point P the largest?
A) Situation A
B) Situation B
C) Situation C
D) Situation D

In the figure, point A is a distance L away from a point charge Q. Point B is a distance 4L away from Q. What is the ratio of the electric field at B to that at A, EB/EA?
A) 1/16
B) 1/9
C) 1/4
D) 1/3
E) This cannot be determined since neither the value of Q nor the length L is specified.

Five particles are shot from the left into a region that contains a uniform electric field. The numbered lines show the paths taken by the five particles. A negatively charged particle with a charge -3Q follows path 2 while it moves through this field. Do not consider any effects due to gravity. Which path would be followed by a charge +6Q?
Path 1
Path 2
Path 3
Path 4
Path 5

Three charges are arranged along the x-axis: +q at x = -2d; +2q at x = d; –4q at x = 2d. Which expression gives the magnitude of the electric field at the origin (x = 0)? In the expressions below, the constant 1/(4πϵ0) has been replaced with k.
A. 5kq / 4d2
B. 11kq / 4d2
C. 13kq / 4d2
D. 3kq / 4d2

A charge of 3 μC is at the origin. Sketch the function E x versus x for both positive and negative values of x. (Remember that Ex is negative when E points in the negative x direction.)

An electron traveling along the +x-axis enters an electric field that is directed vertically down, i.e. along the negative y-axis. What will be the direction of the electric force acting on the electron after entering field?A) downwardB) upwardC) to the leftD) to the right

A charge q1 = +5.0 x 10-9 C is located at the origin of an xy-coordinate system, and a charge q2 = -2.0 x 10-9 c is located on the y-axis at y = 0.3 m. Find the components of the electric field at a point P with coordinates (0.4 m, 0.3 m).

What is the direction of the electric field at the dot?

1. In which case does the electric field at the dot have the largest magnitude? A, B, C, or D2. Three point charges are arranged as shown in the figure below.Which arrow best represents the direction of the electric field vector at the position of the dot? A, B, C, D, or E

What can you say about the field at point 1 compared with the field at point 2?a. The field at point 1 is zero, because point 1 is not on a field line.b. The field at point 2 is larger, because point 2 is on a field line.c. The field at point 1 is larger, because the field lines are closer together in that region.d. The field at point 1 is larger, because point 1 is not on a field line.

Find the electric field at the origin, point O. Give the x and y components of the electric field as an ordered pair. Express your answer in newtons per coulomb to three significant figures. Keep in mind that an x component that points to the right is positive and a y component that points upward is positive.

Three negative point charges lie along a line as shown in the figure. Find the magnitude of the electric field this combination of charges produces at point P, which lies 6.00 cm from the -2.00 μC charge measured perpendicular to the line connecting the three charges. (E = N/C)Find the direction of the electric field this combination of charges produces at point P, which lies 6.00 cm from the -2.00 μC charge measured perpendicular to the line connecting the three charges. outward or inward -2.00 μC?

A point charge q1 = -4.00 nC is at the point x = 0.600 meters, y = 0.800 meters, and a second point charge q2 = +6.00 nC is at the point x = 0.600 meters, y = 0. A) Calculate the magnitude E of the net electric field at the origin due to these two point charges.B) What is the direction, relative to the negative x-axis, of the net electric field at the origin due to these two point charges?

A +16 nC charge is located at the origin.a. What is the strength of the electric field at the position (x,y)=(5.0cm, 0cm)?b. What is the strength of the electric field at the position (x,y)=(5.0cm, 5.0cm)?c. What is the strength of the electric field at the position (x,y)=(-5.0cm, 5.0cm)?

Two point charges are placed on the x-axis. The first charge, q1 = 8.00 nC, is placed a distance 16.0 m from the origin along the positive x-axis; the second charge, q2 = 6.00 nC, is placed a distance 9.00 m from the origin along the negative x-axis.(a) Calculate the electric field at point A, located at coordinates (0 m, 12.0 m).(b) Give the x and y components of the electric field as an ordered pair.Express your answer in newtons per coulomb to three significant figures.EAx, EAy =

What are the strength and direction of the electric field at the position indicated by the dot in figure (Figure 1)A) Give your answer in terms of the horizontal and vertical components. Take the positive directions to be up and to the right.B) Give your answer as a magnitude and angle measured from the positive x-axis.

In the figure, the point charges are located at the corners of an equilateral triangle 21 cm on a side. Part (a) Find the magnitude of the electric field in N/C at the location of qa given that qb=10.8 uC and qc=4.8 uC. Part (b) Find the direction of the electric field at qa, in degrees above the negative x-axis with origin at qaPart (c) What is the magnitude of the force in N on qa given that qa=1.9 nC?Part (d) What is the direction of the force on qa, in degrees above the negative x-axis with origin at qa?

What magnitude charge creates a 1.0 N/C electric field at a point 1.0 m away?

In the figure, the point charges are located at the corners of an equilateral triangle 26 cm on a side.Find the magnitude of the electric field, in newtons per coulomb, at the center of the triangular configuration of charges, given that qa = 1.9 nC, qb = -8.7 nC, and qc = 1.5 nC.

Two positive point charges q are placed on the x-axis, one at x = a and one at x = -a.(a) Find the magnitude and direction of the electric field at x = 0.(b) Derive an expression for the electric field at points on the x -axis. Use your result to graph the x-component of the electric field as a function of x, for values of x between -4a and +4a.

In the figure, the point charges are located at the corners of an equilateral triangle 22 cm on a side.A.) Find the magnitude of the electric field in N/C at the location of qa given that qb = 11.1 μC and qc = -5.3 μCB.) Find the direction of the electric field at qa in degrees above the negative x-axis with origin at qa.

What are the magnitude and direction of the electric field at the dot in Figure below, in which d = 5 cm and theta = 47°?in units of V/m (degree measured counterclockwise from the +x-axis)

Finding the Zero-Field PointTwo particles with positive charges q1 and q2 are separated by a distance s.Along the line connecting the two charges, at what distance from the charge q1 is the total electric field from the two charges zero?Express your answer in terms of some or all of the variables s, q1, q2 and k=1/4πϵ0. If your answer is difficult to enter, consider simplifying it, as it can be made relatively simple with some work.

A proton is released from rest at the positive plate of a parallel-plate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 45000 m/s.What will be the final speed of an electron released from rest at the negative plate?Express your answer to two significant figures and include the appropriate unitsV=_________

(a) Find the direction and magnitude of an electric field that exerts a 4.80x10-17 N westward force on an electron. (b) What magnitude and direction force does this field exert on a proton?

A force of 10 N acts on a charge of 5.0 μC when it is placed in a uniform electric field. What is the magnitude of this electric field?A) 1.0 MN/C B) 50MN/C C) 0.50 MN/C D) 1000 MN/C E) 2.0 MN/C

Figure 18.57 shows an electron passing between two charged metal plates that create an 100 N/C vertical electric field perpendicular to the electron's original horizontal velocity. (These can be used to change the electron's direction, such as in an oscilloscope.) The initial speed of the electron is 3.00×106 m/s, and the horizontal distance it travels in the uniform field is 4.00 cm. (a) What is the vertical deflection?(b) What is the vertical component of its final velocity? (c) At what angle does it exit? Neglect any edge effects.

(a) What is the strength of the electric field at the position indicated by the dot in the figure?(b) What is the direction of the electric field at the position indicated by the dot in the figure? Specify the direction as an angle above the horizontal line.

A free negative charge released in an electric field willa) remain at rest.b) accelerate in a direction perpendicular to the electric field.c) accelerate in the same direction as the electric field is pointing. d) accelerate along a circular path.e) accelerate in the direction opposite the electric field.

A proton is placed in a uniform electric field of 2950 N/C.A. Calculate the magnitude of the electric force felt by the proton.(F = ? )B. Calculate the proton's acceleration.( a= ? m/s2 )C. Calculate the proton's speed after 1.40 in the field, assuming it starts from rest. ( V= ? m/s )

Figure 17.44 shows an electron passing between two charged metal plates that create an 100 N/C vertical electric field perpendicular to the electron's original horizontal velocity. (These can be used to change the electron's direction, such as in an oscilloscope.) The initial speed of the electron is 1.00 × 106 m/s, and the horizontal distance it travels in the uniform field is L = 10.0 cm.(a) What is its vertical deflection?(b) What is the vertical component of its final velocity?(c) At what angle does it exit? Neglect any edge effects.

An electron is projected with an initial speed 1.20×106 m/s into the uniform field between the parallel plates in the figure. Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates. If the electron just misses the upper plate as it emerges from the field, find the speed of the electron as it emerges from the field?

Part ASpecify the strength of the electric field. Let r = 6.5 cm.Part BSpecify the direction.

The figure (Figure 1) shows a thin rod of length L with total charge Q. Find an expression for the electric field E at distance X from the end of the rod. Give your answer in component form. Express your answer in terms of the variables Q, L, X, unit vectors i, j, and appropriate constants.

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