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11 July, 13:42

A very long solid cylinder is made from a material in which the net charge density is constant. The electric field within the cylinder is proportional to: A) r 3 B) r 2 C) r D) constant E) 1/r

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  1. 11 July, 17:40
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    C) r

    Explanation:

    Let ρ be volume charge density of the solid charged cylinder. It is constant

    To know the electric field inside the cylinder, we shall carve out a gaussian surface of cylindrical shape of radius r and length l of the size of length of cylinder.

    The electric field will be axially symmetrical. Let it be E

    Electric flux over curved surface of the cylinder

    = 2πr l x E

    Charge inside the Gaussian surface

    q = πr² l x ρ

    According to Gauss's theorem

    2πr l x E = q / ε

    = πr² l x ρ / ε

    E = ρ r / 2ε

    E is proportional to r. option C is correct.
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