5. From Gauss’s law, the electric field set up by a uniform line of charge is E S 5 a l 2pP0r b r^ where r^ is a unit vector pointing radial

Question

5. From Gauss’s law, the electric field set up by a uniform line of charge is E S 5 a l 2pP0r b r^ where r^ is a unit vector pointing radially away from the line and l is the linear charge density along the line. Derive an expression for the potential difference between r 5 r1 and r 5 r2.

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Adela 5 months 2021-08-21T21:56:19+00:00 1 Answers 3 views 0

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    2021-08-21T21:57:55+00:00

    Answer:

     ΔV = 2k λ ln (r₁ / r₂)

    Explanation:

    The electric potential is

             ΔV = – ∫ E. ds

    The expression for the electric field of a charge line is given

               E = 2k λ / r

    Let’s replace and integrate

             ΔV = – 2k λ ∫ dr / r

             ΔV = -2 k λ ln r

    Let’s evaluate

           ΔV = – 2k λ ln r₂- ln r₁

           ΔV = -2k λ ln (r₂ / r₁)

           ΔV = 2k λ ln (r₁ / r₂)

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