Practice: How far from a 5uC charge will the potential be 100 V?

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Practice: How far from a 5uC charge will the potential be 100 V?

Practice: A -1uC and a 5uC charge lie on a line, separated by 5cm. What is the electric potential halfway between the two charges?

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Concept #1: Electric Potential

Example #1: Movement of Charges in Potential Fields

Concept #2: Potential Due To Point Charges

Practice #1: Electric Potential due to Point Charge

Practice #2: Potential Between Two Point Charges

Example #2: Potential Difference Between Two Charges

Three charges of magnitude |q| = 3.0 x 10-9C are placed along the circumference of a circle with radius R = 1.0m. A charge +q lies at x = -R, a charge -q at y = -R, and a charge -q at x = R.
a. Determine the electric potential at the origin of the circle.
b. If a negative charge with q = -1.5 x 10-9 C brought from r= ∞ and placed at the origin, what is the change in potential energy of the system of charges?

Two particles, with charges of 20.0 nC and -20.0 nC, are located at the points with coordinates (0, 4.00 cm) and (0, -4.00 cm), as shown in the figure below. A third particle with charge 40.0 nC is located at the point (5.00 cm, 0).
Determine the electrical potential at the origin (0,0) due to the three fixed charges (40.0 nC, 20.0 nC, and -20.0 nC).

Two particles, with charges of 20.0 nC and –20.0 nC, are located at the points with coordinates (0, 4.00 cm) and (0, – 4.00 cm), as shown in the figure below. A third particle with charge 10.0 nC is located at the origin (0,0). Determine the electric potential at the point (3.00 cm, 0) due to the three fixed charges (10.0 nC, 20.0 nC, and –20.0 nC).

A 4.0-μC charge is situated at the origin of an xy-coordinate system. What is the potential difference between a point x = 4.0 m and y = -4.0 m because of this charge?
A) -18×103 V
B) 18×103 V
C) 0 V
D) 36×103 V

Which statement below, describing an electrostatic situation of a conductor, is NOT correct?
A) The electric field within a conductor is zero.
B) The electric potential within a conductor is equal everywhere.
C) The electric field outside of a conductor is always perpendicular to the surface.
D) Excess charges of a conductor only reside below the surface, not on the surface.

Consider a square with sides L = 48cm and two negative charges Q = - 2.5 μC placed on the corners labeled with Q in the figure. What is the electric potential in the corner of the square labeled by B?

Two charged spherical conductors are connected by a long conducting wire. A total charge of q > 0 is placed on this combination of two spheres. Sphere 1 has a radius of r1 and sphere 2 has a radius of r2, where r2 > r1. If q1 represents the charge on sphere 1 and q 2 the charge on sphere 2, what is the ratio q1 / q2 of the charges?
1. q1 / q2 = r2 / r1
2. q1 / q2 = r1 / r1 + r2
3. q1 / q2 = (r2 / r1)2
4. q1 / q2 = r2 / r1 + r2
5. None of these
6. q1 / q2 = 1
7. q1 / q2 = (r1 / r2)2
8. q1 / q2 = r1 / r2

Three point charges are held on the circumference of a circle of radius 20 cm as shown in the figure. Assume that the electric potential is defined to be zero at infinity. Determine the electric potential at the center of the circle.
(a) +6.0 x 104 V
(b) +2.3 x 105 V
(c) -4.6 x 105 V
(d) –7.8 x 105 V
(e) zero volts

Let: V = 0 at infinity. Three charges are arranged in the (x, y) plane (as shown in the figure below, where the scale is in meters). Find the electric potential Vo at the origin [coordinates (0 m, 0 m)].

A sphere with radius 2.0 mm carries a 2.0 μC charge. What is the potential difference, VB - VA, between point B 4.0 m from the center of the sphere and point A 6.0 m from the center of the sphere? (The value of k is 9.0x109 N•m2/C2.)A) 1500 VB) -0.63 VC) -1500 VD) 170 V

The electric potential at a point that is halfway between two identical charged particles is 300 V. What is the potential at a point that is 25% of the way from one particle to the other?

A disk with radius R has uniform surface charge density σ.By regarding the disk as a series of thin concentric rings, the electric potential V at a point on the disk's axis a distance x from the center of the disk is Derive an expression for −∂V/∂x.Express your answer in terms of the given quantities and appropriate constants.

a) Which direction (clockwise or counterclockwise) does conventional current travel through the wire in the figure to the right? Explain. b) At which point (a or b) will an electron feel more electric potential? Explain. c) At which point (a or b) will an electron have more electric potential energy? Explain.

A single point charge in vacuum has imaginary equipotential surfaces around it which are spherical due to the symmetry of the situation. Assume we have a charge q = 2.5x10-10 C and such a surface with potential V = 38 V.Part (a) Input an expression for the radius for this surface, r, in terms of the given quantitiesPart (b) What is the radius, in meters?Part (c) What is the radius, in meters, if a 10,000 V equipotential surface?

a. Which point, A or B, has a larger electric potentialb. What is the potential difference between A and B? Assume that E=1500V/m

a. What is the electric potential at points A, B, and C in the figure?b. What is the potential energy of an electron at point A in the figure?c. What is the potential energy of an electron at point B in the figure?d. What is the potential energy of an electron at point C in the figure?e. What is the potential difference ΔVAB?f. What is the potential difference ΔVBC?

A point charge is released from rest in a region containing an electric field. The charge will start to move: (A) in a direction that makes its potential energy increase (B) in a direction that makes its potential energy decrease (C) along a path of constant potential energy (D) Either A or B, depending on the sign of the point chargeA point charge is released from rest in a region containing an electric field. The charge will start to move: (A) in a direction of increasing electric potential (B) in a direction of decreasing electric potential (C) along a path of constant electric potential (D) Either A or B, depending on the sign of the point charge

A positive and negative charge are shown in (Figure 1) .At which numbered position (or positions) is the electric potential zero?

A -10.0nC point charge and a +20.0nC point charge are 15.0cm apart on the x-axis.a) What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero? b) What is the direction of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

What is the electric potential at the point indicated with the dot in the figure? Express your answer to two significant figures and include the appropriate units.

What is the electric potential at the point indicated with the dot in the figure below? Suppose that q = 1.4 nC.

The figure shows a thin rod with charge Q that has been bent into a semicircle of radius R.Find an expression for the electric potential at the center.Give your answer in terms of Q, R and appropriate constants.

A ring with radius R and a uniformly distributed total charge Q lies in the xy plane, centered at the origin.Part A. What is the potential V(z) due to the ring on the z axis as a function of z? Express your answer in terms of Q, z, R, and ε0 or k = 1/(4πε0) Part B. What is the magnitude of the electric field E on the z axis as a function of z, for z > 0? Express your answer in terms of some or all of the quantities Q, z, R, and ε0 or k = 1/(4πε0)

Rank the electric potentials at the four points shown in the figure below from largest to smallest. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)

What is the electric potential at the point indicated with the dot in the figure? (Figure 1)Express your answer using two significant figures.

Part A. Find the electric potential at point P in the figure. VP =________VPart B. Suppose the three charges shown in the figure are held in place. A fourth charge, with a charge of +7.00 µC and a mass of 4.80 g, is released from rest at point P. What is the speed of the fourth charge when it has moved infinitely far away from the other three charges? v =________m/s

A proton has an initial speed of 3.9 × 105 m/s.What potential difference is required to bring the proton to rest?_____ kV

A proton has an initial speed of 3.9 × 105 m/s.What potential difference is required to reduce the initial speed of the proton by a factor of 3?

A 1.50 mm-diameter glass bead is positively charged. The potential difference between a point 1.50 mm from the bead and a point 3.60 mm from the bead is 460V.Note: The given distances are measured from the surface of the bead.What is the charge on the bead?

Two points, point 1 and point 2, are located inside a region with an electric field pointing to the left, as shown in the figure. Part (a) If a proton is moved from point 1 to point 2, how will the potential energy of the charge-field system change? How will the potential change?Part (b) If, instead, an electron is moved from point 1 to point 2, how will the potential energy of the charge-field system change? How will the potential change?

A 2.0mm -diameter ball bearing has 5.0 x 109 excess electrons. What is the ball bearing's potential?

A -3.0 nC charge is on the x-axis at x = -9 cm and a +4.0 nC charge is on the x-axis at x = 15 cm. At what point or points on the y-axis is the electric potential zero?y = _____ cm

Suppose you have a fixed charge of -15.0 nC at point X. Points A and B are at distances of 20.0 cm and 40.0 cm from X as shown. Calculate the following:a) the potential at points A and Bb) the potential difference between A and Bc) the potential energy of a proton at A and Bd) the speed at point B of a proton that was moving to the right at point A with a speed of 4.0 × 105 m/se) the speed at point A of a proton that was moving to the left at point B with a speed of 1.0 × 105 m/s.

Pictured on the right are thee point charges Q1 = 21.4 μC, Q2 = -30.6 μC, and Q3 = 57.3 μC arranged according to the figure on the right. Calculate the potential at point A in the figure.

Three point charges are arranged at the corners of a square of side L as shown in (Figure 1) What is the potential at the fourth corner (point A)? Express your answer in terms of the variables Q, L, and the Coulomb's constant k.

a. What is the potential difference ΔVAB?b. What is the potential difference ΔVBC?

A hollow spherical conductor, carrying a net charge +Q, has inner radius r1 and outer radius r2=2r1 (see the figure (Figure 1)). At the center of the sphere is a point charge +Q/2. Plot V as a function of r from r=0 to r=2r2. Assume V0=3Q/8πϵ0r2.

In the diagram below, there are two charges of +q and - q and six points (a through f) at various distances from the two charges (figure 1) You will be asked to rank changes in the electric potential along paths between pairs of points. Using the diagram, rank each of the given paths on the basis of the change in electric potential. Rank the largest-magnitude positive change (increase in electric potential) as largest and the largest-magnitude negative change (decrease in electric potential) as smallest. Rank from largest to smallest. To rank items as equivalent, overlap them

a) If a proton moved from a location with 5.0v potential to a location with 7.5v potential, would its potential energy increase or decrease? b) If an electron moved from a location with 7.5v potential to a location with 5.0v potential, would its potential energy increase or decrease? Explain in detail.

Two stationary positive point charges, charge 1 of magnitude 3.90 nC and charge 2 of magnitude 1.80 nC, are separated by a distance of 46.0 cm. An electron is released from rest at the point midway between the two charges, and it moves along the line connecting the two charges.What is the speed vfinal of the electron when it is 10.0 cm from charge 1?

Two point charges q1 = 2.00 nC and q2 = -6.20 nC are 0.100 m apart. Point A is midway between them; point B is 0.080 m from q1 and 0.060 m from q2 (the figure ). Take the electric potential to be zero at infinity.a. Find the potential at point A. b. Find the potential at point B. c. Find the work done by the electric field on a charge of 2.00 nC that travels from point B to point A.

You are designing a Van de Graaff generator, and you want it to hold as many electrons as possible. Should you make the radius of the sphere very large or very small?

The two halves of the rod in the figure are uniformly charged to plus/minus Q as shown.What is the electric potential at the point indicated by the dot?

The figure is a graph of Ex. The potential at the origin is -300 V.What is the potential at x = 3.0 m?

a. What is the electric potential at point A in the figure above?b. What is the potential energy of a proton at point A?

5 V battery with metal wires attached to each end.What are the potential differences ΔV12=V2−V1, ΔV23=V3−V2, ΔV34=V4−V3, and ΔV41=V1−V4?

What is the potential difference VAB = VA − VB between points A and B?Express your answer in terms of some or all of E, x1, y1, x2, and y2.

It takes 4.0 μJ of work to move a 19 nC charge from point A to B. It takes -6.5 μJ of work to move the charge from C to B. What is the potential difference VC−VA? Express your answer using two significant figures.

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