In a certain region of space,electric field is along the z-direction throughout. The magnitude of electric field is however not constant, but increases uniformly along the positive z-direction at the rate of $10^{5} N C^{- 1} m^{- 1}$ . The force experienced by the system having a total dipole moment equal to $10^{- 7} C$ $m$ in the negative z-direction is

- 10^{- 2} N

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10^{- 2} N

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10^{- 4} N

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- 10^{- 4} N

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Solution

The correct option is A $- 10^{- 2} N$
Consider an electric dipole dipole with $- q$ charge at $A$ and $+ q$ charge at $B$ , placed along z-axis, that its dipole moment is in negative $z$ direction
i.e, $p_{z} = - 10^{- 7} C m$
The electric field is along positive direction of z-axis, such that
$\frac{d E}{d z} = 10^{5} N C^{- 1} m^{- 1}$
From $F = q d E = (q \times d z) \times \frac{d E}{d z} = p \frac{d E}{d z}$
$∴ F = - 10^{- 7} \times 10^{5} = - 10^{- 2} N$

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