If V and u are electric potential and energy density, respectively, at a distance r from a positive point charge, then which of the following graphs is correct?

Question

If V and u are electric potential and energy density, respectively, at a distance r from a positive point charge, then which of the following graphs is correct? (A) Option 1

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

textV=( textitkQ/ textitr) we know that, u=(1/2)ϵ 0 textitE2=(1/2)(ϵ 0 k2 Q2/r4) ∴ textV4 propto u

Q. If $V$ and $u$ are electric potential and energy density, respectively, at a distance $r$ from a positive point charge, then which of the following graphs is correct?

$V = \frac{kQ}{r}$
we know that,
$u = \frac{1}{2} ϵ_{0} E^{2} = \frac{1}{2} \frac{ϵ _{0} k ^{2} Q ^{2}}{r ^{4}}$
$∴$ $V^{4} \propto u$

Q. If V and u are electric potential and energy density, respectively, at a distance r from a positive point charge, then which of the following graphs is correct?

V=rkQ​ we know that, u=21​ϵ0​E2=21​r4ϵ0​k2Q2​ ∴ V4∝u

Q. If $V$ and $u$ are electric potential and energy density, respectively, at a distance $r$ from a positive point charge, then which of the following graphs is correct?

$V = \frac{kQ}{r}$
we know that,
$u = \frac{1}{2} ϵ_{0} E^{2} = \frac{1}{2} \frac{ϵ _{0} k ^{2} Q ^{2}}{r ^{4}}$
$∴$ $V^{4} \propto u$