JEE Main 2022 — Physics Electromagnetism

2022mcqmedium

Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$ . Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at midpoint between spheres $A$ and $B$ . The force experienced by sphere $C$ will be :

Official previous-year question

Held on 29 Jul 2022 · Verified 6 Jul 2026.

Options

A
$\frac{3F}{2}$
B
$\frac{3F}{4}$
C
$F$
D
$2F$

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Solution

Let charge on $A$ and $B$ be ${q}_{A}={q}_{B}=q$ .

JEE Main 2022 Physics, Electrostatics — solution figure 1

Then force acting between them is $F=\frac{K{q}^{2}}{{r}^{2}}$ .

When $C$ is placed in contact with $A$ , charge on $A$ and $C$ will be $=\frac{q}{2}$

Now $C$ is placed in contact with $B$ , charge on $B$ and $C$ will be $=\frac{q+\frac{q}{2}}{2}=\frac{3q}{4}$

Now, force experienced by sphere $C$ is

JEE Main 2022 Physics, Electrostatics — solution figure 2

${F}^{'}={F}_{2}-{F}_{1} =\frac{K9{q}^{2}}{16\times \frac{{r}^{2}}{4}}-\frac{K3{q}^{2}}{8\times \frac{{r}^{2}}{4}} =\frac{(K\frac{3q}{4}-K\frac{q}{2})}{\frac{{r}^{2}}{4}}\times \frac{3q}{4}$

$=\frac{3K{q}^{2}}{4{r}^{2}}=\frac{3F}{4}$

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Solution

Let charge on $A$ and $B$ be ${q}_{A}={q}_{B}=q$ .

JEE Main 2022 Physics, Electrostatics — solution figure 1

Then force acting between them is $F=\frac{K{q}^{2}}{{r}^{2}}$ .

When $C$ is placed in contact with $A$ , charge on $A$ and $C$ will be $=\frac{q}{2}$

Now $C$ is placed in contact with $B$ , charge on $B$ and $C$ will be $=\frac{q+\frac{q}{2}}{2}=\frac{3q}{4}$

Now, force experienced by sphere $C$ is

JEE Main 2022 Physics, Electrostatics — solution figure 2

${F}^{'}={F}_{2}-{F}_{1} =\frac{K9{q}^{2}}{16\times \frac{{r}^{2}}{4}}-\frac{K3{q}^{2}}{8\times \frac{{r}^{2}}{4}} =\frac{(K\frac{3q}{4}-K\frac{q}{2})}{\frac{{r}^{2}}{4}}\times \frac{3q}{4}$

$=\frac{3K{q}^{2}}{4{r}^{2}}=\frac{3F}{4}$

JEE Main 2022 — Physics Electromagnetism

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JEE Main 2022 — Physics Electromagnetism

Options

Did you get this right?

Solution

Your note

JEE Main Electromagnetism in other years

More JEE Main Electromagnetism questions

Other Physics topics for JEE Main

Mechanics

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Electromagnetism