Question

The magnetic field at the centre of a current carrying circular loop is B. If the radius of the loop
is doubled, keeping the current as same the magnetic field at the centre of the loop would be
​

Answer 1

Answer:

B/2

As Magnetic Field at center

B = u°I/2R

B ~ 1/R

Radius doubled Than B half

Answer 2

Answer:

Magnetic field at the centre of loop reduces to half, if the radius of loop is doubled.

Explanation:

• Considering, a current carrying loop of radius, r having current, I. The magnetic field at the centre of the loop is

$B = \frac{μ₀I}{2r}$

• where, μ₀ is permeability of free space.
• If the current carrying loop has N turns, then magnetic field at the centre of loop is

$B = \frac{Nμ₀I}{2r}$

• The magnetic field due to a current carrying loop at its centre varies inversely with radius, r and directly with current flowing through that loop.
• If we double the radius of the loop, magnetic field at the centre of loop becomes

$B' = \frac{μ₀I}{2(2r)} = \frac{μ₀I}{4r} \\ B' = \frac{B}{2}$

• Hence, magnetic field at the centre of loop reduces to half, if the radius of loop is doubled.