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Chapter 25: Q.54 (page 712)

A 2.0-mm-diameter glass bead is positively charged. The potential difference between a point 2.0 mm from the bead and a point 4.0 mm from the bead is 500 V. What is the charge on the bead?

Short Answer

Expert verified

The charge on the bead isq=1.39·10-13C.

Step by step solution

01

Step 1. Given information

A 2.0-mm-diameter glass bead is positively charged. The potential difference between a point 2.0 mm from the bead and a point 4.0 mm from the bead is 500 V .

02

Step 2.Simplify

We'll use the same old "trick" that you have hopefully mastered by now: consider the potential on the surface of the sphere to be the potential created by a point charge at a distance equal to the radius of the sphere. This allows us to write down our given potential difference as

ΔV=kq1r-1r+d.
03

Step 3. Finding the charge

Where ris the radius of the bead, d is the distance from the bead in which the potential falls by ΔVand q is the charge we're looking for. We can find the latter as

ΔV=kqr+d-rr(r+d)q=r(r+d)ΔVkd

Numerically, in our case, we'll have

q=0.001(0.001+0.004)9·109·0.004=1.39·10-13C

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