A current carrying circular loop of radius 50 mm, made of a very thin wire has inductance 0.26 `mu`H and is placed in the uniform magnetic field 0,5 mT. The plane of the loop is perpendicular to the magnetic field lines. The resistance of loop can be neglected. Now the magnetic field has been turned off. Find the current in the loop (approximately)

Options

A. 30A
B. 15 A
C. 10A
D. 0A

Answer

To find the induced current in a circular loop when the magnetic field is turned off, we can use the relationship between magnetic flux, inductance, and current. Here’s a step-by-step solution:

### Step 1: Understand the Given Information
- **Radius of the loop (R)** = 50 mm = 0.05 m
- **Inductance (L)** = 0.26 µH = 0.26 × 10⁻⁶ H
- **Magnetic field (B)** = 0.5 mT = 0.5 × 10⁻³ T
- The resistance of the loop can be neglected.

### Step 2: Calculate the Area of the Loop
The area (A) of a circular loop is given by the formula:
\[ A = \pi R^2 \]
Substituting the radius:
\[ A = \pi (0.05)^2 = \pi (0.0025) \approx 0.007854 \text{ m}^2 \]

### Step 3: Calculate the Magnetic Flux (Φ)
The magnetic flux (Φ) through the loop is given by:
\[ \Phi = B \cdot A \]
Substituting the values:
\[ \Phi = (0.5 \times 10^{-3}) \cdot (0.007854) \approx 3.927 \times 10^{-6} \text{ Wb} \]

### Step 4: Relate Inductance, Current, and Magnetic Flux
The relationship between inductance (L), current (I), and magnetic flux (Φ) is given by:
\[ \Phi = L \cdot I \]
Rearranging this to find the current:
\[ I = \frac{\Phi}{L} \]

### Step 5: Substitute the Values to Find Current
Substituting the values of Φ and L:
\[ I = \frac{3.927 \times 10^{-6}}{0.26 \times 10^{-6}} \approx 15.096 \text{ A} \]

### Step 6: Round the Answer
The current can be approximated to:
\[ I \approx 15 \text{ A} \]

### Final Answer
The induced current in the loop when the magnetic field is turned off is approximately **15 A**.

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