At a distance d from a point charge Q,the energy density in its electric field is u.If we double the charge,what is the energy density at the same point?

Question

Quizplus · Accepted Answer

The energy density at a distance d from a point charge Q is given by
$$U=\frac{1}{2}\epsilon_0 E^2=\frac{1}{2}\epsilon_0 \left(\frac{Q}{4\pi\epsilon_0 d^2}\right)^2=\frac{Q^2}{32\pi\epsilon_0 d^2}$$
If we double the charge to 2Q, then the energy density at the same point becomes
$$U'=\frac{(2Q)^2}{32\pi\epsilon_0 d^2}=\frac{4Q^2}{32\pi\epsilon_0 d^2}=4U$$
Therefore, the energy density is quadrupled or becomes 4 times larger. The correct choice is C) 4u.

At a Distance D from a Point Charge Q,the Energy 2\sqrt { 2 }2​

At a Distance D from a Point Charge Q,the Energy $\sqrt { 2 }$