Question

If current through a single circular loop of radius 10 cm produces a magnetic field of \( B \, \text{Tesla} \) at the centre, what is the current through the loop?

Hint:

The magnetic field at the centre of a circular loop depends on the radius and the current flowing through the loop. Use the formula \( B = \frac{\mu_0 I}{2r} \) to find the current.

Answer 1

The magnetic field at the centre of a circular loop of radius \( r \) carrying a current \( I \) is given by the formula: \[ B = \frac{\mu_0 I}{2r} \] where:
- \( B \) is the magnetic field at the centre of the loop,
- \( \mu_0 \) is the permeability of free space (\( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \)),
- \( I \) is the current, and
- \( r \) is the radius of the loop.
Step 1: Rearrange the formula to solve for current.
Rearrange the equation to solve for the current \( I \): \[ I = \frac{2rB}{\mu_0} \]
Step 2: Substitute the given values.
We are given:
- \( r = 10 \, \text{cm} = 0.1 \, \text{m} \),
- \( B = \mu_0 \, \text{Tesla} \),
- \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \).
Substitute these values into the equation: \[ I = \frac{2 \times 0.1 \times \mu_0}{\mu_0} = 0.2 \, \text{A} \] Thus, the current through the loop is: \[ \boxed{0.2 \, \text{A}} \]