Magnetic Fields

Question

For a long straight wire, if the current is halved and the distance from the wire is doubled, what will B be then?

Answer 1

The magnetic field strength B at a perpendicular distance r from a long straight wire with current i is given by Ampere's law as

 

B = μ₀i / (2πr)

 

If you replace i with i/2 and r with 2r you get

 

B' = μ₀(i/2) / [2π(2r)] = (1/4) [μ₀i / (2πr)] = B/4

 

B' = B/4