Potential Difference with Calculus Video Lessons

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Problem: What is the electric potential at the center of the semicircle?Give your answer in terms of λ, R, ϵ 0 and appropriate constant

FREE Expert Solution

The electric potential:

V=kqr

The charge carried by the piece of wire is given by,

dq=λdx, where λ is the linear charge density.

To calculate the electric potential at the center of the semicircle due to the right wire:

dVright = kdq/x

Integrating both sides from x = R to 3R:

Vright=R3R(kdqx)=R3R(kλdxx)=kλ[lnx]R3R

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Problem Details

What is the electric potential at the center of the semicircle?

Give your answer in terms of λ, R, ϵ 0 and appropriate constant

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