Question

An electric dipole with dipole moment (4* 10– 9)Cm is aligned at 30 degree with the direction of a uniform electric field of magnitude (5 *104 ) newton per coulomb calculate the magnitude of the torque acting on the dipole? (3)

Answer 1

$\checkmark$ Given:

An electric dipole with dipole moment 4 x 10⁻⁴ C m is aligned at 30° with

the direction of a uniform electric field of magnitude 5  x 10⁴  NC⁻¹

$\checkmark$ To Find:

The magnitude of the torque acting on the dipole

$\checkmark$ Solution:

We know that,

$\red{\bigstar \ \boxed{\sf \tau=pE \sin \theta}}$

Here,

• τ = Torque
• p = Dipole-moment
• E = Electric field

According to the Question,

We are asked to find the magnitude of the torque acting on the dipole

So,we must find "τ"

Given that,

An electric dipole with dipole moment 4 x 10⁻⁴ C m is aligned at 30° with

the direction of a uniform electric field of magnitude 5  x 10⁴  NC⁻¹

Hence,

• p = 4 x 10⁻⁴ C m
• E = 5  x 10⁴  NC⁻¹
• θ = 30°

Substituting the values,

We get,

$\blue{\implies \sf \tau=4 \times 10^{-9} \times 5 \times 10^{4} \times \sin30^{\circ}}$

We know that,

$\red{\sf \longrightarrow \sin 30^{\circ}=\dfrac{1}{2}}$

Hence,

Substituting that value,

We get,

$\green{\sf \implies \tau=20 \times 10^{-5} \times \dfrac{1}{2} \ N \ m}$

$\orange{\sf \implies \tau=10 \times 10^{-5} \ N \ m}$

$\pink{\sf \implies \tau= 10^{-4} \ N \ m}$

Therefore,

The magnitude of the torque acting on the dipole is 10⁻⁴ N m

Answer 2

Given ,

Dipole moment (P) = 4 x 10⁻⁴ C-m

Electric field (E) = 5 x 10⁴ N/C

Angle b/w P and E = 30°

We know that , the torque on a electric dipole in the uniform electric field is given by

$\boxed{ \sf{Torque \: (τ) = PE \sin( \theta) }}$

Thus ,

τ = 4 x 10^(-9) × 5 x 10^(4) × sin(30)

τ = 20 × 10^(-5) × 1/2

τ = 10 × 10^(-5)

τ = 10^(-4) N-m

Therefore ,

• The magnitude of the torque acting on the dipole is 10^(-4) N-m