Question

potential V and distance x are related as V = x2 - 4 volt, the electric field E at x = 1 meter will be

(a) Zero
(b) infinity
(c) 2Vm-1
(d) -2 Vm-1​

Answer 1

Voltage is related to Displacement as follows:

$V = {x}^{2} - 4$

$\implies \: E = - \dfrac{dV}{dx}$

$\implies \: E = - \dfrac{d( {x}^{2} - 4) }{dx}$

$\implies \: E = - 2x$

$\implies \: E \bigg|_{x = 1} = - 2 \times 1$

$\implies \: E \bigg|_{x = 1} = - 2 \: V {m}^{ - 1}$

So, field intensity is -2 V/m.