Question

An electric dipole is made up of two equal and opposite charges of 2 × $10^{-6}$C at a distance of 3cm. If this is kept in an electric field of 2 × $10^5$ N/C, then the maximum torque acting on the dipole is $P$ × $10^{-3}$ Nm. Find the value of $P$.

Answer 1

12

Answer 2

The maximum torque ($\tau_{max}$) acting on an electric dipole in an electric field (E) is given by the formula:

$\tau_{max} = pE$

where $p$ is the electric dipole moment.

The electric dipole moment ($p$) is calculated as the product of the magnitude of one of the charges ($q$) and the distance ($l$) between the two charges:

$p = ql$

Given values:

• Charge, $q = 2 \times 10^{-6}$ C
• Distance between charges, $l = 3$ cm $= 3 \times 10^{-2}$ m
• Electric field, $E = 2 \times 10^5$ N/C

First, calculate the electric dipole moment ($p$):

$p = (2 \times 10^{-6} \text{ C}) \times (3 \times 10^{-2} \text{ m})$

$p = (2 \times 3) \times (10^{-6} \times 10^{-2}) \text{ C}\cdot\text{m}$

$p = 6 \times 10^{-8} \text{ C}\cdot\text{m}$

Next, calculate the maximum torque ($\tau_{max}$):

$\tau_{max} = pE$

$\tau_{max} = (6 \times 10^{-8} \text{ C}\cdot\text{m}) \times (2 \times 10^5 \text{ N/C})$

$\tau_{max} = (6 \times 2) \times (10^{-8} \times 10^5) \text{ N}\cdot\text{m}$

$\tau_{max} = 12 \times 10^{-3} \text{ N}\cdot\text{m}$

The problem states that the maximum torque is $P \times 10^{-3}$ Nm.

By comparing our calculated value with the given form:

$P \times 10^{-3} \text{ Nm} = 12 \times 10^{-3} \text{ Nm}$

Therefore, $P = 12$.