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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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Most popular questions from this chapter

Two positive point charges q are located on the y-axis aty=±12s.

a.Find an expression for the potential along the x-axis.

b.Draw a graph of V versus x for -∞<x<∞. For comparison, use a dotted line to show the potential of a point charge 2qlocated at the origin.

What is the electric potential energy of the group of charges in FIGURE EX25.6?

A capacitor with plates separated by distance dis charged to a potential difference ∆VC. All wires and batteries are disconnected, then the two plates are pulled apart (with insulated handles) to a new separation of distance2d.
a. Does the capacitor chargeQ change as the separation increases?
If so, by what factor? If not, why not?
b. Does the electric field strengthEchange as the separation increases? If so, by what factor? If not, why not?
c. Does the potential difference ∆VCchange as the separation increases? If so, by what factor? If not, why not?

A proton is released from rest at the positive plate of a parallelplate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000m/s. The experiment is repeated with aHe+ ion (charge e, mass4u ). What is the ion's speed at the negative plate?

In a semiclassical model of the hydrogen atom, the electron

orbits the proton at a distance of 0.053 nm.

a. What is the electric potential of the proton at the position of the electron?

b. What is the electron’s potential energy?
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