Question

Calculate the electric field at x = 2 given the electric potential at this point is ϕ=3x3.

Answer 1

Hi there!

Recall the following relationship:
$E = -\frac{dV}{dx}$

E = Electric field strength (V/m)
V = Potential Difference (V)

Take the derivative of the given electric potential equation using the power rule:
$\frac{d}{dx}x^n = nx^{n-1}$

$-\frac{dV}{dx} = -(3 \cdot 3 \cdot x^2) = -9x^2$

Evaluate at x = 2:
$E(2) = -9(2^2) = \boxed{-36 \frac{V}{m}}$

**The magnitude of the field strength would simply be 36 V/m.