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A thin circular ring has a radius R and charge3 Q distributed uniformly over its length. What is the electric potential at the center of the ring? Hint: this is very easy since every point on the ring is the same distance from the center. Therefore you don't need to integrate. а. P 3Q, R b. What is the electric potential at a distance z along the axis of the thin ring? Comment: each point on the ring is still the same distance from point P. 3Q, R

A thin circular ring has a radius R and charge3 Q distributed uniformly over its length. What is the electric potential at the center of the ring? Hint: this is very easy since every point on the ring is the same distance from the center. Therefore you don't need to integrate. а. P 3Q, R b. What is the electric potential at a distance z along the axis of the thin ring? Comment: each point on the ring is still the same distance from point P. 3Q, R

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3. A thin circular ring has a radius R and charge3 Q distributed uniformly over its length. What is the electric potential at the center of the ring? Hint: this is very easy since every point on the ring is the same distance from the center. Therefore you don't need to integrate. а. 3Q, R b. What is the electric potential at a distance z along the axis of the thin ring? Comment: each point on the ring is still the same distance from point P. 3Q, R
Transcribed Image Text:3. A thin circular ring has a radius R and charge3 Q distributed uniformly over its length. What is the electric potential at the center of the ring? Hint: this is very easy since every point on the ring is the same distance from the center. Therefore you don't need to integrate. а. 3Q, R b. What is the electric potential at a distance z along the axis of the thin ring? Comment: each point on the ring is still the same distance from point P. 3Q, R
Expert Solution
Step 1 a

lets take a small element on ring of length dl, and charge on this element is dq.

linear charge density on ring λ=QL=3Q2πR

charge on small element dq=λdl

now potential due to a small charge dq at distance R, dV=kdqR

all the element on ring are at same distance from center.

potential due to ring on it's center

 V=∫dV=∫02πRkdqR           =∫02πRkλdlR           =kλ(2π)         V =3kQR

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