Question

Assume that an electric field E=30x²i exists in space. Then the potential difference Va-Vo, where Vo is the potential at the origin and Va the potential at x=2m is

Answer 1

Given that,

Electric field in the space, $E=30x^2i$

To find,

The potential difference Va-Vo, where Vo is the potential at the origin and Va the potential at x = 2 m.

Solution,

The relation between electric field and electric potential is given by :

$dV=-Edx$

Integrating both sides we get :

$\int\limits^{V_a}_{V_o}dV=\int\limits^2_0 {-30x^2} \, dx$

So, it would become :

$V_a-V_o=-30x[\dfrac{x^3}{3}]^2_0\\\\V_a-V_o=-10(2^3-0^3)\\\\V_a-V_o=-80\ V$

So, the potential difference is (-80 V).