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Chapter 24: Q7P (page 710)

The electric field in a region of space has the components Ey = Ez = 0and Ex = (4.00N/C)x. Point Ais on the yaxis at y = 3.00m, and point Bis on the xaxis at x = 4.00m. What is the potential difference VB - VA?

Short Answer

Expert verified

The potential difference is, -32.0V.

Step by step solution

01

Given

The electric field in a region of space has the components Ey = Ez = 0 and Ex = (4.00N/C)x.

02

Understanding the concept

Using the equation of potential difference V = E.d, we can find the potential difference between two points.

03

Calculate the potential difference VB - VA

We connect A to the origin with a line along the y axis, along which there is no change of potential (Equation: ∫E.ds=0). Then, we connect the origin to B with a line along the x-axis, along which the change in potential is

∆V=-∫0x=4E.ds

Substitute all the value in the above equation.

∆V=-4.00∫04xdx=-4.00x2204VB-VA=-4.00422VB-VA=-32.0V

Hence the potential difference is, -32.0V.

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Most popular questions from this chapter

A Gaussian sphere of radius 4.00cm is centered on a ball that has a radius ofrole="math" localid="1662731665361" 1.00cm and a uniform charge distribution. The total (net) electric flux through the surface of the Gaussian sphere is+5.6×104N⋅m2/C . What is the electric potential 12.0cmfrom the center of the ball?

A particular 12Vcar battery can send a total charge of 84 A.h(ampere-hours) through a circuit, from one terminal to the other. (a) How many coulombs of charge does this represent? (Hint:See Eq. 21-3.) (b) If this entire charge undergoes a change in electric potential of 12 V, how much energy is involved?

Question: What is the escape speedfor an electron initially at rest on the surface of a sphere with a radius ofand a uniformly distributed charge of1.6×10-15C? That is, what initial speed must the electron have in order to reach an infinite distance from the sphere and have zero kinetic energy when it gets there?

Sphere 1 with radius has positive charge . Sphere 2 with radius is far from sphere 1 and initially uncharged. After the separated spheres are connected with a wire thin enough to retain only negligible charge, (a) is potential of sphere 1 greater than, less than, or equal to potential of sphere 2? What fraction of ends up on (b) sphere 1 and (c) sphere 2? (d) What is the ratio of the surface charge densities of the spheres?

Question: Two particles of chargesq1and q2 , are separated by distance in Fig. 24-40. The net electric field due to the particles is zero at x = d/4 .With V = 0 at infinity, locate (in terms of ) any point on the x-axis (other than at infinity) at which the electric potential due to the two particles is zero.
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