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Chapter 25: Q. 73 (page 713)

The wire in FIGURE P25.73 has linear charge density λ. What is the electric potential at the center of the semicircle?

Short Answer

Expert verified

The electric potential at the center of the semicircle isV=kλ(2In(3)+π).

Step by step solution

01

Given Information

We need to find the electric potential at the center of the semicircle.

02

Simplify

The potential at the point of interest will be the sum of potentials coming from the straight lines and the curved section. By symmetry, it is clear that the potential coming from the two straight segments are equal. So, we can calculate one of them, and the potential coming from both will be twice in our result.

Therefore, we can write

V=k2∫02Rλdzx+R+∫0πRλdxR

Factorizing the linear charge density, we can simplify

V=kλ∫02Rdxx+R+1R∫0πRdx

The result will be

kλ2In3R-InR+π=kλ2In3+π

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Most popular questions from this chapter

Electrodes of area Aare spaced distance dapart to form a parallel-plate capacitor. The electrodes are charged to ±q.

(a). What is the infinitesimal increase in electric potential energy dUif an infinitesimal amount of charge dqis moved from the negative electrode to the positive electrode?

(b). An uncharged capacitor can be charged to ±Qby transferring charge dqover and over and over. Use your answer to part a to show that the potential energy of a capacitor charged to ±Qis Ucap=12QΔVC.

A proton’s speed as it passes point A is 50,000 m/s. It follows the trajectory shown in FIGURE P25.43. What is the proton’s speed at point B? A proton’s speed as it passes point A is 50,000 m/s. It follows the trajectory shown in FIGURE P25.43. What is the proton’s speed at point B?

A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder ?

Three electrons form an equilateral triangle with 1.0 nm on each side. A proton is at the center of the triangle. What is the potential energy of this group of charges?

Through what potential difference must a proton be accelerated to reach the speed it would have by falling 100min vacuum?
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