A bar magnet when placed at an angle of 30° to the direction of magnetic field induction of 5 × 10⁻² T, experiences a moment of couple 25 × 10⁻⁶ N·m. If the length of the magnet is 5cm its pole strength is

• 2 × 10⁻² A − m
• 5 × 10⁻² A − m
• 2 A − m
• 5 A − m

To find the pole strength of the bar magnet, we can use the formula for the moment of couple (τ) acting on a magnet in a magnetic field:

Formula for Moment of Couple

The moment of couple is given by:

τ = m × B × sin(θ)

• τ = moment of couple (N·m)
• m = magnetic moment (A·m²)
• B = magnetic field induction (T)
• θ = angle between the magnet and the magnetic field (degrees)

Given Values

• τ = 25 × 10⁻⁶ N·m
• B = 5 × 10⁻² T
• θ = 30°
• Length of the magnet (l) = 5 cm = 0.05 m

Calculating the Magnetic Moment

First, we need to calculate the sine of the angle:

sin(30°) = 0.5

Now, substituting the values into the formula:

25 × 10⁻⁶ = m × (5 × 10⁻²) × 0.5

Solving for m:

m = (25 × 10⁻⁶) / (5 × 10⁻² × 0.5)

m = (25 × 10⁻⁶) / (2.5 × 10⁻²) = 1 × 10⁻³ A·m²

Finding the Pole Strength

The magnetic moment (m) is also related to the pole strength (p) and the length of the magnet (l) by:

m = p × l

Substituting the known values:

1 × 10⁻³ = p × 0.05

Solving for p gives:

p = (1 × 10⁻³) / 0.05 = 0.02 A·m

Final Answer

The pole strength of the magnet is 2 × 10⁻² A·m.