Two charges q_1 and q_2 are separated by a distance of 30 cm. A...

Two charges

\mathrm{q}_1

and

\mathrm{q}_2

are separated by a distance of 30 cm. A third charge

q_3

initially at ' C ' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of

q_3

from

C

D

is given by

\frac{\mathrm{q}_3 \mathrm{~K}}{4 \pi \epsilon_0}

, the value of K is :
Two charges q_1 and q_2 are separated by a distance of 30 cm. A third charge q_3 initially at ' C ' as shown in the

Options

A $8 \mathrm{q}_2$
B $6 \mathrm{q}_2$
C $8 q_1$
D $6 \mathrm{q}_1$

Correct answer

A. $8 \mathrm{q}_2$

Step-by-step solution

Potential at C

\mathrm{V}_{\mathrm{C}}=\frac{\mathrm{kq}_1}{0.4}+\frac{\mathrm{kq}_2}{0.5}

Potential at D

\mathrm{V}_{\mathrm{D}}=\frac{\mathrm{kq}_1}{0.4}+\frac{\mathrm{kq}_2}{0.1}

\Delta \mathrm{U}=\left(\mathrm{V}_{\mathrm{D}}-\mathrm{V}_{\mathrm{c}}\right)\left(\mathrm{q}_3\right)=\left(\frac{\mathrm{kq}_2}{0.1}-\frac{\mathrm{kq}_2}{0.5}\right)\left(\mathrm{q}_3\right)

\Delta \mathrm{U}=8 \mathrm{kq}_2 \mathrm{q}_3=\frac{8 \mathrm{q}_2 \mathrm{q}_3}{4 \pi \varepsilon_0}

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