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JEE Main 202431 JanuaryEvening Shift
Exam
JEE Main
Year
2024
Date
31 January
Shift
Evening Shift
Subject
Physics
Chapter
Electrostatics

JEE Main 2024 · 31 January · Evening Shift · Physics · Electrostatics

The distance between charges + q and - q is 2l and between + 2q and...

The distance between charges +q+ q and −q- q is 2l2l and between +2q+ 2q and −2q- 2q is 4l4l. The electrostatic potential at point PP at a distance rr from centre OO is −α[qlr2]×109V- \alpha\left[\dfrac{ql}{{r}^{2}}\right] \times {10}^{9}V, where the value of α\alpha is ______. (Use 14πε0=9×109Nm2C−2\dfrac{1}{4\pi{ε}_{0}} = 9 \times {10}^{9}N{m}^{2}{C}^{- 2})

The distance between charges + q and - q is 2l and between + 2q and - 2q is 4l . The electrostatic potential at point P

Correct answer

0

Step-by-step solution

Considering two dipoles with charges 2q and q2q \text{ and } q, we can write the equivalent setup as shown below:

The distance between charges + q and - q is 2l and between + 2q and - 2q is 4l . The electrostatic potential at point P

Therefore, net dipole moment is Pnet=6ql{P}_{net} = 6ql in the leftward direction.

The distance between charges + q and - q is 2l and between + 2q and - 2q is 4l . The electrostatic potential at point P

Potential required, 

V=Kp→⋅r→r3=9×109(6ql)r2cos⁡(120o)V = \dfrac{K\overset{\to}{p} \cdot \overset{\to}{r}}{{r}^{3}} = \dfrac{9 \times {10}^{9}\left(6ql\right)}{{r}^{2}}\cos \left({120}^{o}\right)

=−(27)(qlr2)×109= - \left(27\right)\left(\dfrac{ql}{{r}^{2}}\right) \times {10}^{9}

Therefore, α=27\alpha = 27.

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