Question

Find the potential difference between a point on the axis and a point on the outer cylinder. Note that it is not necessary to commit yourself to a particular reference point.

Answer 1

Answer:

$V(b)-V(a) = - \int\limits^b_a {E} \, dL$

Explanation:

Solution:

- The Electric potential V is given as line integral(L) of Electric Field E. The expression.

                                 $V = -\int\limits^r_0 {E} \, dL$

Where, r is the radial distance from the axis of charged body.

- The coaxial cable has inner radius (a) and outer radius (b). The potential difference between the inner radius (a) and outer radius (b) can be expressed as follows:

                             $V(b)-V(a) = - \int\limits^b_0 {E} \, dL + \int\limits^a_0 {E} \, dL \\\\V(b)-V(a) = - \int\limits^b_0 {E} \, dL - \int\limits^0_a {E} \, dL\\\\V(b)-V(a) = - \int\limits^b_a {E} \, dL$