A Rectangular coil of 10 turns, each of area 0.05 `m^(2)`, is suspended freely in a uniform magnetic field of induction 0.01 T. A current of 30 µA is passed through it. (i) What is the magnetic moment of the coil (ii) What is the maximum torque experienced by the coil?

Answer

To solve the problem step by step, we will break it down into two parts: calculating the magnetic moment of the coil and then finding the maximum torque experienced by the coil.

### Step 1: Calculate the Magnetic Moment (M) of the Coil

The formula for the magnetic moment (M) of a coil is given by:

\[ M = N \times I \times A \]

Where:
- \( N \) = number of turns of the coil = 10
- \( I \) = current flowing through the coil = 30 µA = \( 30 \times 10^{-6} \) A
- \( A \) = area of the coil = 0.05 m²

Now substituting the values into the formula:

\[ M = 10 \times (30 \times 10^{-6}) \times 0.05 \]

Calculating this step by step:

1. Calculate \( 30 \times 10^{-6} \):
\[ 30 \times 10^{-6} = 0.000030 \, \text{A} \]

2. Now calculate \( 10 \times 0.000030 \):
\[ 10 \times 0.000030 = 0.0003 \]

3. Finally, multiply by the area:
\[ M = 0.0003 \times 0.05 = 0.000015 \, \text{A m}^2 \]

Thus, the magnetic moment \( M \) is:

\[ M = 15 \times 10^{-6} \, \text{A m}^2 \]

### Step 2: Calculate the Maximum Torque (τ)

The formula for the maximum torque (τ) experienced by the coil in a magnetic field is given by:

\[ \tau_{\text{max}} = N \times I \times A \times B \]

Where:
- \( B \) = magnetic field induction = 0.01 T

Using the previously calculated magnetic moment \( M \):

\[ \tau_{\text{max}} = M \times B \]

Substituting the values:

\[ \tau_{\text{max}} = (15 \times 10^{-6}) \times 0.01 \]

Calculating this:

1. Multiply \( 15 \times 10^{-6} \) by \( 0.01 \):
\[ \tau_{\text{max}} = 15 \times 10^{-6} \times 0.01 = 15 \times 10^{-8} \]

So, we can express it as:

\[ \tau_{\text{max}} = 1.5 \times 10^{-7} \, \text{N m} \]

### Final Answers

1. The magnetic moment of the coil is \( 15 \times 10^{-6} \, \text{A m}^2 \).
2. The maximum torque experienced by the coil is \( 1.5 \times 10^{-7} \, \text{N m} \).