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Three charges -q1, +q2 and -q3 are place...

Three charges `-q_1`, `+q_2` and `-q_3` are placed as shown in the figure. The x-component of the force on `-q_1` is proportional to

A

(a) `(q_2)/(b^2)-(q_3)/(a^2)cos theta`

B

(b) `(q_2)/(b^2)+(q_3)/(a^2)sin theta`

C

(c) `(q_2)/(b^2)+(q_3)/(a^2) cos theta`

D

(d) `(q_2)/(b^2)-(q_3)/(a^2) sin theta`

Text Solution

Verified by Experts

The correct Answer is:
B
Force on charge `q_1` due to `q_2` is `F_(12)=k(q_1q_2)/(a^2)`
Force on charge `q_1` due to `q_3` is `F_(13)=k(q_1q_3)/(a^2)`
The X-component of the force `(F_x)` on
`q_1` is `F_(12)+F_(13) sin theta`
`:.` `F_x=k(q_1q_2)/(b^2)+k(q_1q_2)/(a^2)sintheta`
`:.` `F_xprop(q_2)/(b^2)+(q_3)/(a^2)sin theta`
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