Question

The energy density in the electric field created by a point charge falls off with the distance from the point charge as
(a) 1r
(b) 1r2
(c) 1r3
(d) 1r4.

Answer 1

answer : option (d) 1/r⁴

The electric field density is given as, U = $\frac{1}{2}\epsilon_0E^2$

where $\epsilon_0$ is permittivity of vaccum and E is the electric field.

here it is clear that, U ∝ E² ......(1)

from Coulomb's law,

electric field, E = Kq/r²

means, electric field is inversely proportional to r².

i.e., E ∝ 1/r² .........(2)

from equations (1) and (2) we get,

U ∝ (1/r²)² ⇒U ∝ 1/r⁴

i.e., energy density is inversely proportional to r⁴.

option (d) is correct choice.

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Answer 2

$\huge\bold\purple{Answer:-}$

(d) 1r4.