The current through the circular coil is halved and the radius of the coil is doubled. If B₁ and B₂ are respectively the initial and final magnetic field strength, then:

Step-by-step solution

The magnetic field at the center of a circular coil is given by B = ₀ I 2R . Initial magnetic field is B₁ = ₀ I 2R . The current is halved, so I' = I 2 . The radius is doubled, so R' = 2R . Final magnetic field is B₂ = ₀ I' 2R' = ₀ ( I 2 ) 2(2R) = 1 4 ( ₀ I 2R ) . Therefore, B₂ = B₁ 4 . Answer: B₂ = B₁ 4