A dipole with two electric charges of 2 C magnitude each, with separation distanve 0.5 m, is placed between the plates of a capacitor such that its axis is parallel to an electric feild established between the plates when a potential difference of 5 V is

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Solution

Q.
A dipole with two electric charges of 2 $μ$ C magnitude each, with separation distance 0.5 $μ$ m, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30° from the axis, it tends to realign in the direction due to a torque. The value of torque is : [2025]

1 $5 \times 10^{- 9} Nm$

2 $5 \times 10^{- 3} Nm$

3 $2.5 \times 10^{- 12} Nm$

4 $2.5 \times 10^{- 9} Nm$

Ans.
(1)

$E = \frac{V}{d} = \frac{5}{5 \times 10^{- 4}} = 10^{4} V / m$

$τ = PE \sin θ$

Where $P = q a = 2 \times 10^{- 6} \times 5 \times 10^{- 7} = 1 \times 10^{- 12} C - m$

$τ = 1 \times 10^{- 12} \times 10^{4} \times \frac{1}{2} = 5 \times 10^{- 9} N - m$

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