Question

3.
Two opposite and equal charges 4 x 10°C when placed
dipole is placed in an external electric field 4 * 10% N/C, the value of maximum torque and the work
done in rotating it through 180° will be : (a) 64 × 10 -4 N-m and 64 x 104 J (b) 32 x 10 * N-m and 64
x 1041 (C) 64 x 104 N-m and 32 x 104 J (d) 32 x 104 N-m and 64 x 104 J.
f rodiny s and having same charge q are combined to form a big drop. The
1:1) 2:1 (d) 1:8​

Answer 1

Given that,

Charge $q=4\times10^{-8}\ C$

Distance $d=2\times10^{-2}\ cm$

Electric field $E=4\times10^{8}\ N/C$

We need to calculate the value of dipole

Using formula of dipole

$P=qd$

Put the value into the formula

$P=4\times10^{-8}\times2\times10^{-4}$

$P=8\times10^{-12}\ C-m$

We need to calculate the maximum torque

Using formula of torque

$\vec{\tau}=\vec{P}\times \vec{E}$

Put the value into the formula

$\tau=8\times10^{-12}\times4\times10^{8}$

$\tau=32\times10^{-4}\ N-m$

We need to calculate the work done

Using formula of work done

$W=PE(1-\cos\theta)$

$W=8\times10^{-12}\times4\times10^{8}(1-\cos\theta)$

$W=0.0064\ J$

$W=64\times10^{-4}\ J$

Hence, The maximum torque is $32\times10^{-4}\ N-m$

The work done is $64\times10^{-4}\ J$