25. Electric Potential

Electric Potential

Finding the Electric Potential due to Two Point Charges

(a) How much excess charge must be placed on a copper sphere 25.0 cm in diameter so that the potential of its center, rela­tive to infinity, is 3.75 kV? (b) What is the potential of the sphere’s surface relative to infinity?

Two stationary point charges +3.00 nC and +2.00 nC are separated by a distance of 50.0 cm. An electron is released from rest at a point midway between the two charges and moves along the line connecting the two charges. What is the speed of the electron when it is 10.0 cm from the +3.00-nC charge?

Metal sphere A is charged until it has a potential of <math display=“inline”><mrow><mn>200</mn><mtext>&#x00A0;</mtext><mi mathvariant="normal">V</mi></mrow></math>. Metal sphere B is initially uncharged, and has a radius twice the radius of sphere A. A small wire is used to connect spheres A and B, so that they form one continuous equipotential surface. What is the final potential on the surface of sphere B?

Potential Due To Point Charges

Two point charges q_1 = +2.40 nC and q_2 = -6.50 nC are 0.100 m apart. Point A is midway between them; point B is 0.080 m from q_1 and 0.060 m from q_2 (Fig. E23.19). Take the electric potential to be zero at infinity. Find (b) the potential at point B.<img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/e611795e25d93983-1678286443050.jpg" style="width: 228px;">

A uniform electric field with strength <math display=“inline”><mrow><mn>12</mn><mtext>&#x00A0;</mtext><mi mathvariant="normal">V</mi><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></math> points from point A to point B, which are on the x-axis: <math display=“inline”><mrow><msub><mi>x</mi><mtext>A</mtext></msub><mo>=</mo><mrow><mn>45</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math> and <math display=“inline”><mrow><msub><mi>x</mi><mi mathvariant="normal">B</mi></msub><mo>=</mo><mrow><mn>12</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math>. What is the potential difference <math display=“inline”><mrow><msub><mi>V</mi><mtext>A</mtext></msub><mo>&#x2212;</mo><msub><mi>V</mi><mi mathvariant="normal">B</mi></msub></mrow></math>?

How far from a 5μC charge will the potential be 100 V?

Two large, parallel conducting plates carrying op­posite charges of equal magnitude are separated by 2.20 cm. (a) If the surface charge density for each plate has magnitude 47.0 nC/m^2, what is the magnitude of E in the region between the plates?

A small particle has charge -5.00 μC and mass 2.00x10^-4 kg. It moves from point A, where the electric po-tential is V_A = +200 V, to point B, where the electric potential is V_B = +800 V. The electric force is the only force acting on the particle. The particle has speed 5.00 m/s at point A. What is its speed at point B? Is it moving faster or slower at B than at A? Explain.

Two point charges of equal magnitude Q are held a distance d apart. Consider only points on the line passing through both charges. (a) If the two charges have the same sign, find the location of all points (if there are any) at which (i) the potential (relative to infinity) is zero (is the electric field zero at these points?), and (ii) the electric field is zero (is the potential zero at these points?).

At a certain distance from a point charge, the poten-tial and electric-field magnitude due to that charge are 4.98 V and 16.2 V/m, respectively. (Take V = 0 at infinity.) (a) What is the distance to the point charge?

Anderson Video - Electric Potential Units

An electron is to be accelerated from 3.00x10^6 m/s to 8.00x10^6 m/s. (a) Through what potential difference must the electron pass to accomplish this?

A positive charge q is fixed at the point x = 0, y = 0, and a negative charge -2q is fixed at the point x = a, y = 0. (a) Show the positions of the charges in a diagram.

A thin spherical shell with radius R_1 = 3.00 cm is concentric with a larger thin spherical shell with radius R_2 = 5.00 cm. Both shells are made of insulating material. The smaller shell has charge q_1 = +6.00 nC distributed uniformly over its surface, and the larger shell has charge q_2 = -9.00 nC distributed uniformly over its surface. Take the electric potential to be zero at an infinite distance from both shells. (a) What is the electric potential due to the two shells at the following distance from their common center: (i) r=0; (ii) r=4.00 cm; (iii) r=6.00 cm?

Physics - E&M: Ch 38.1 Voltage Potential Understood (9 of 24) Potential Due to Multiple Charges%%%

Two point charges q_1 = +2.40 nC and q_2 = -6.50 nC are 0.100 m apart. Point A is midway between them; point B is 0.080 m from q_1 and 0.060 m from q_2 (Fig. E23.19). Take the electric potential to be zero at infinity. Find (a) the potential at point A.<img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/e132b3ad445df7a1-1678286444794.jpg" style="width: 261px;">

An infinitely long line of charge has linear charge den­sity 5.00x10^-12 C/m. A proton (mass 1.67x10^-27 kg, charge +1.60x10^-19 C) is 18.0 cm from the line and moving directly toward the line at 3.50x10^3 m/s. (a) Calculate the proton’s initial kinetic energy.

Anderson Video - Electric Potential Intro

At a certain distance from a point charge, the poten-tial and electric-field magnitude due to that charge are 4.98 V and 16.2 V/m, respectively. (Take V = 0 at infinity.) (b) What is the magnitude of the charge?

Two large, parallel conducting plates carrying op­posite charges of equal magnitude are separated by 2.20 cm. The surface charge density for each plate has magnitude 47.0 nC/m^2. (c) If the separation between the plates is doubled while the surface charge density is kept constant at the given value, what happens to the magnitude of the electric field and to the po­tential difference?

At a certain distance from a point charge, the poten-tial and electric-field magnitude due to that charge are 4.98 V and 16.2 V/m, respectively. (Take V = 0 at infinity.) (c) Is the electric field directed toward or away from the point charge?

What is the electric potential 3.0 cm away from a <math display=“inline”><mrow><mo>&#x2212;</mo><mn>12</mn><mtext>&#x00A0;</mtext><mtext>nC</mtext></mrow></math> point charge?

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

<math display=“inline”><mrow><mi>x</mi><mo>=</mo><mrow><mn>0.67</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></mrow></math> only

<math display=“inline”><mrow><mi>x</mi><mo>=</mo><mrow><mn>0.83</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></mrow></math> only

<math display=“inline”><mrow><mi>x</mi><mo>=</mo><mrow><mn>1.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></mrow></math> only

A <math display=“inline”><mrow><mo>&#x2212;</mo><mn>9.0</mn><mtext>&#x00A0;</mtext><mtext>nC</mtext></mrow></math>charge sits at the origin, and a <math display=“inline”><mrow><mo>+</mo><mn>18</mn><mtext>&#x00A0;</mtext><mtext>nC</mtext></mrow></math> charge is at <math display=“inline”><mrow><mi>x</mi><mo>=</mo><mrow><mn>2.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></mrow></math>. At what location(s) is the potential zero?

Point charges q_1 = +2.00 μC and q_2 = -2.00 μC are placed at adjacent corners of a square for which the length of each side is 3.00 cm. Point a is at the center of the square, and point bis at the empty corner closest to q_2. Take the electric potential to be zero at a distance far from both charges. (a) What is the electric potential at point a due to q_1 and q_2?

Potential Difference Between Two Charges

What is an Electric Potential ?

Movement of Charges in Potential Fields

A spherical balloon is charged so that the potential on its surface is <math display=“inline”><mrow><mn>40</mn><mtext>&#x00A0;</mtext><mi mathvariant="normal">V</mi></mrow></math>. The balloon is now deflated to half its original radius (with no loss of charge). What is the new potential on its surface?

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