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Chapter 15: Q5Q (page 616)

A student claimed that the equation for the electric field outside a cube of edge length L, carrying a uniformly distributed charge Q, at a distancex from the center of the cube, was

role="math" localid="1668495301957" E=Qε0Lx1/2

Explain how you know that this cannot be the right equation.

Short Answer

Expert verified

The claimed equation is incorrect because it gives incorrect dimension of electric field.

Step by step solution

01

Identification of given data

The formula for electric field outside a cube of edge length L, carrying a uniformly distributed charge Q, at a distance xfrom the center of the cube is claimed by a student to be

Ec=Qε0Lx1/2

02

Dimensions of electric field and permittivity

The dimension of electric field is

[E]=M1L1T-3I-1 …(i)

The dimension of permittivity is

[ε0]=M-1L-3T4I2 …(ii)

03

Determination of the correctness of the claimed formula

The dimension of the claimed formula, using equation (ii), is

Ec=Q1ε0-1L1x-1/2=I1T1×M-1L-3T4I2-1×L1×L-1/2=ML7/2T-3I-1

This does not match. Hence the formula is incorrect due to incorrect dimension.

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Most popular questions from this chapter

In Figure 15.61 are two uniformly charged disks of radius R that are very close to each other (gap≪R). The disk on the left has a charge of−Qleftand the disk on the right has a charge of +Qright(Qrightis greater thanQleft). A uniformly charged thin rod of length L lies at the edge of the disks, parallel to the axis of the disks and cantered on the gap. The rod has a charge of +Qrod.

(a) Calculate the magnitude and direction of the electric field at the point marked × at the center of the gap region, and explain briefly, including showing the electric field on a diagram. Your results must not contain any symbols other than the given quantities R,Qleft, Qright, L, andQrod(and fundamental constants), unless you define intermediate results in terms of the given quantities. (b) If an electron is placed at the center of the gap region, what are the magnitude and direction of the electric force that acts on the electron?

What is wrong with Figure 15.35 and this associated incorrect student explanation? “The electric field at location inside the uniformly charged sphere points in the direction shown, because the charges closest to this location have the largest effect.” (Spheres provide the most common exception to the normally useful rule that the nearest charges usually make the largest contribution to the electric field.)

Two rings of radius 2 cm are 20 cm apart and concentric with a common horizontal x axis. What is the magnitude of the electric field midway between the rings if both rings carry a charge of +35 nC?

A rod is 2.5m long. Its charge is -2×10-7C. The observation location is 4cm from the rod, in the mid plane. In the expression

E=14πε0Qrr2+(L2)2

what isr in meters?

Question: A thin hollow spherical glass shell of radius carries a uniformly distributed positive charge +6×10-9C, as shown in Figure 15.65. To the right of it is a horizontal permanent dipole with charges +3×10-11and -3×10-11separated by a distance (the dipole is shown greatly enlarged for clarity). The dipole is fixed in position and is not free to rotate. The distance from the center of the glass shell to the center of the dipole is 0.6 m.

(a) Calculate the net electric field at the center of the glass shell. (b) If the sphere were a solid metal ball with a charge , what would be the net electric field at its center? (c) Draw the approximate charge distribution in and/or on the metal sphere.
See all solutions

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