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Two point charges of magnitude +q and -q...

Two point charges of magnitude `+q and -q` are placed at `(-d//2,0,0) and (d//2,0,0)` are respectively. Find the equation of the euipotential surface where the potential is zero.

A

`z^2 + (y-a)^2 = 2a`

B

`z^2 + (y-a)^2 = 27a^2//4`

C

`z^2+y^2 = 15a^2//4`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
c. As in none of the options, the `x-`cordinate appears, so we have to find the locus in the `yz` plane.

`U=(kQ^(2))/(r_(1))-(kQ^(2))/(r_(2))-(kQ^(2))/(r_(3))=0`
`kQ^(2)[(1)/(a)-(1)/(sqrt((a//2)^(2)+y^(2)+z^(3)))-(1)/(sqrt((a//2)^(2)+y^(2)+z^(3)))]=0`
`(1)/(a)=(2)/(sqrt(a^(2)//4+y^(2)+z^(2))` or `y^(2)+z^(3)=15a^(2)//4`
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