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Show mathematically that the potential a...

Show mathematically that the potential at a point on the equatorial line of an electric dipole is zero.

Text Solution

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Consider a point P situated on the equatorial line of the electric dipole at a distance r from mid-point of dipole.
Now electric potential at P is given by
`V = V_A + V_B = (-q)/ (4 pi epsi_0 sqrt(r^2 + a^2)) + q/(4pi epsi_0 sqrt(r^2 + a^2)) = 0` .
hus, potential at any point on equatorial line of an electric -9. dipole is zero irrespective of the position of that point.
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Knowledge Check

  • The electric potential at a point on the equatorial line of a electric dipole is

    A
    directly proportional to the square of the distance
    B
    indirectly proportional to the square of the distance
    C
    directly proportional to the charge
    D
    none of the above

  • Assertion (A): Electric potenital at any point on the equatroial line of an electric dipoel is zero Reason (R ) :Electrons potential is scalar

    A
    Both `(A)` and `(R )` are true and `'R'` is the correct explanation of `A`.
    B
    Both `A` and `R` are true and `R` is not the correct explanation of `A`
    C
    `A` is true and `R` is false
    D
    `A` is false and `R` is true.

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    Deive an expression for the electric field at any point on the equatorial line of an electric dipole.

    (a) Derive and expression for the electric field at any point on the equatorial line of an electric dipole. (b) Two identical point charges, q each kept 2m apart in air. A third point charge Q of unknown magnitude and sign is placed on the line joining the charges such that the system remains in equilibrium. Find the position and nature of Q.

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