Question

A 1.2-m radius cylindrical region contains a uniform electric field along the cylinder axis. It is increasing uniformly with time. To obtain a total displacement current of 2.0x10-­9 A through a cross section of the region, the magnitude of the electric field should change at a rate of:

Answer 1

Answer:

The magnitude of rate of change of electric field is $49.95\ V/m{\cdot} s$.

Explanation:

Given that,

Radius of the cylindrical region contains a uniform electric field along the cylinder axis, r = 1.2 m

Total displacement current through a cross section of the region, $I=2\times 10^{-9}\ A$

We need to find the rate of change of electric field. Its is given by the formula as follows :

$\dfrac{dE}{dt}=\dfrac{I}{A\epsilon_o}\\\\\dfrac{dE}{dt}=\dfrac{2\times 10^{-9}}{\pi (1.2)^2\times 8.85\times 10^{-12}}\\\\\dfrac{dE}{dt}=49.95\ V/m{\cdot} s$

So, the magnitude of rate of change of electric field is $49.95\ V/m{\cdot} s$.