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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=Q蔚0Lx1/2

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=Q蔚0Lx1/2

02

Dimensions of electric field and permittivity

The dimension of electric field is

[E]=M1L1T-3I-1 鈥�(颈)

The dimension of permittivity is

[蔚0]=M-1L-3T4I2 鈥�(颈颈)

03

Determination of the correctness of the claimed formula

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

Ec=Q1蔚0-1L1x-1/2=I1T1脳M-1L-3T4I2-1脳L1脳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

A solid metal ball of radius 1.5 cm bearing a charge of 鈭�17 nC is located near a solid plastic ball of radius 2 cm bearing a uniformly distributed charge of +7 nC (Figure 15.62) on its outer surface. The distance between the centers of the balls is 9 cm. (a) Show the approximate charge distribution in and on each ball. (b) What is the electric field at the center of the metal ball due only to the charges on the plastic ball? (c) What is the net electric field at the center of the metal ball? (d) What is the electric field at the center of the metal ball due only to the charges on the surface of the metal ball?

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

E=14蟺蔚0Qrr2+(L2)2

what isr in meters?

Coulomb鈥檚 law says that electric field falls off like 1/z2. How can Efor a uniformly charged disk depend on [1-z/R], or be independent of distance?

Consider a capacitor made of two rectangular metal plates of length L and width W, with a very small gap s between the plates. There is a charge +Qon one plate and a charge 鈭扱on the other. Assume that the electric field is nearly uniform throughout the gap region and negligibly small outside. Calculate the attractive force that one plate exerts on the other. Remember that one of the plates doesn鈥檛 exert a net force on itself

What is wrong with Figure 15.35 and this associated incorrect student explanation? 鈥淭he 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.鈥� (Spheres provide the most common exception to the normally useful rule that the nearest charges usually make the largest contribution to the electric field.)
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