JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Electrostatics

Consider two charged metallic spheres

S_{1}

and

S_{2}

of radii

R_{1}

and

R_{2}

, respectively. The electric fields

E_{1}

(on

S_{1}

) and

E_{2}

(on

S_{2}

) on their surfaces are such that

E_{1} / E_{2} = R_{1} / R_{2}

. Then the ratio of

V_{1}

(on

S_{1}

)

/ V_{2}

(on

S_{2}

) of the electrostatic potentials on each sphere is:

Answer: (A)

Solution

For a charged conducting sphere the surface field and potential are

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

and

V = \frac{k Q}{R}

, so

E = \frac{V}{R}

and

V = E R

. Then

\frac{V _{1}}{V _{2}} = \frac{E _{1} R _{1}}{E _{2} R _{2}} = \frac{E _{1}}{E _{2}} \cdot \frac{R _{1}}{R _{2}}

, and since the data give

\frac{E _{1}}{E _{2}} = \frac{R _{1}}{R _{2}}

, this becomes

\frac{V _{1}}{V _{2}} = (\frac{R _{1}}{R _{2}})^{2}

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Single correct option