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

Electric potential due to a point charge at a point is,

V = \frac{k Q}{r}

Electric potential due to a point charge at a point is,

E = \frac{k Q}{r ^{2}}

We know that, energy density due to electric field,

u = \frac{1}{2} ϵ_{0} E^{2} = \frac{1}{2} \frac{ϵ _{0} k ^{2} Q ^{2}}{r ^{4}}

On replacing

r

,

u = (\frac{1}{2} \frac{ϵ _{0}}{k ^{2} Q ^{2}}) V^{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?

Electric potential due to a point charge at a point is, V=rkQ​ Electric potential due to a point charge at a point is, E=r2kQ​ We know that, energy density due to electric field, u=21​ϵ0​E2=21​r4ϵ0​k2Q2​ On replacing r , u=(21​k2Q2ϵ0​​)V4 ∴ 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?