Question

If the electric potential in a region is given by v(x)=7/x2 the x component of the electric field in that region is

Answer 1

Hi there!

Recall that:
$\Delta V = -\int\limits^a_b {E \cdot } \, dx$

Given an electric field, the potential difference can be solved by using integration. Similarly:
$E = -\frac{dV}{dx}$

We can differentiate the electric potential equation to solve for the electric field.

Use the power rule:
$\frac{dy}{dx} x^n = nx^{n - 1}$

Differentiate the given equation.

$-\frac{dV}{dx}\frac{7}{x^2} =- \frac{dV}{dx}7x^{-2} = -(-14x^{-3}) = \frac{14}{x^3}$

Or:
$\boxed{E(x) = \frac{14}{x^3}}$