A bar magnet of length `10cm` and pole strength `2 Am` makes an angle `60^(0)` with a uniform magnetic field of induction `50T`. The couple acting on it is

Options

A. `5sqrt3Nm`
B. `sqrt3Nm`
C. `10sqrt3Nm`
D. `20sqrt3Nm`

Answer

To find the couple acting on a bar magnet placed in a magnetic field, we can follow these steps:

### Step 1: Understand the given values
- Length of the bar magnet (L) = 10 cm = 0.1 m
- Pole strength (P) = 2 Am
- Angle (θ) = 60°
- Magnetic field induction (B) = 50 T

### Step 2: Calculate the magnetic moment (M)
The magnetic moment (M) of a bar magnet is given by the formula:
\[ M = L \times P \]
Substituting the values:
\[ M = 0.1 \, \text{m} \times 2 \, \text{Am} = 0.2 \, \text{Am}^2 \]

### Step 3: Calculate the torque (τ) acting on the magnet
The torque (τ) acting on a magnetic dipole in a magnetic field is given by the formula:
\[ τ = M \times B \times \sin(θ) \]
Substituting the values we have:
\[ τ = 0.2 \, \text{Am}^2 \times 50 \, \text{T} \times \sin(60°) \]

### Step 4: Calculate sin(60°)
We know that:
\[ \sin(60°) = \frac{\sqrt{3}}{2} \]

### Step 5: Substitute sin(60°) into the torque equation
Now substituting this value into the torque equation:
\[ τ = 0.2 \times 50 \times \frac{\sqrt{3}}{2} \]

### Step 6: Simplify the expression
Now we can simplify:
\[ τ = 0.2 \times 50 \times \frac{\sqrt{3}}{2} = 5\sqrt{3} \, \text{N m} \]

### Final Answer
The couple acting on the bar magnet is:
\[ τ = 5\sqrt{3} \, \text{N m} \]

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