In a long solid wire of radius a, current density varies as J(r)=J₀r/a. If the internal field is written B(r)=μ₀J₀rˣ/(ya), find x+y.
Physics · Magnetic effect of current
JEE Advanced

Question

In a long solid wire of radius a, current density varies as J(r)=J₀r/a. If the internal field is written B(r)=μ₀J₀rˣ/(ya), find x+y.

G1 Physics · Accepted Answer

I enclosed=∫₀ʳ(J₀r′/a)2πr′dr′=2πJ₀r³/(3a). Ampere's law gives B(2πr)=μ₀I enclosed, so B=μ₀J₀r²/(3a). Thus x=2 and y=3, so x+y=5.