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Derive the following.
An electric dipole is kept in a uniform electric field with its axis making an angle with the…
An electric dipole is kept in a uniform electric field $E$ with its axis making an angle $\theta$ with the field. Show forces acting on each charge and hence prove that torque acting is given by
$\tau = pE\sin\theta$
To show: $\tau = pE\sin\theta$
Answer
Answer
Checked answer.
$C = \frac{\epsilon_0 A}{d - t + \frac{t}{K}}$, where A is the area of each plate, d the separation, t the thickness of the slab and K its dielectric constant.
- Let the plates have area A and separation d, carry charges $+Q$ and $-Q$, and let a slab of thickness $t$ and dielectric constant $K$ be placed between them.
- In the air gap (total thickness $d - t$) the field is $E_0 = \frac{\sigma}{\epsilon_0} = \frac{Q}{\epsilon_0 A}$.
- Inside the slab the field is reduced by $K$: $E = \frac{E_0}{K} = \frac{Q}{K \epsilon_0 A}$.
- Potential difference between the plates: $V = E_0 (d - t) + E t = \frac{Q}{\epsilon_0 A}\left(d - t + \frac{t}{K}\right)$.
- Capacitance: $C = \frac{Q}{V} = \frac{\epsilon_0 A}{d - t + \frac{t}{K}}$.
- Since $d - t + \frac{t}{K} < d$, the capacitance is greater than without the slab ($\frac{\epsilon_0 A}{d}$).
From ISC 2027 Specimen Physics Paper 1, question 9(ii).