Magnetic field at a point (x, y, z) is given by B→=B0yx2+y212i^-B0xx2+y212j^ Find current enclosed in the loop - Physics - Moving Charges And Magnetism

Question

Magnetic field at a point (x, y, z) is given by B →
= B 0 y x 2 + y 2 1 2 i ^ - B 0 x x 2 + y 2 1 2 j ^ Find current
enclosed in the loop
x 2 + y 2 = r
2

(1) B 0   r µ 0 (2) 2 B 0   r µ 0 (3) 2
π   B 0   r µ 0 (4) B 0   r 2  
µ 0

Manoj Singh · Accepted Answer

Dear Student,

Use ampere circuital law
∮B dl = μ0Ienclosed    
(1)Use stokes theorem∮B
dl = ∬∇×B ds    
(2)First we calculate ∇×B
    I can not write indermidiate steps
∇×B = k^(-B0r+B0x2r3)-(B0r-B0y2r3) =k^(2B0r+B0r3(x2+y2))   = -B0r k^Applying in 1 equation∮B
dl = ∬-B0r k^
ds=B0r ∬ds = B0rπr2 = B0πrFrom equation 1Ienclosed =  B0πrμ0

Magnetic field at a point (x, y, z) is given by B → = B 0 y x 2 + y 2 1 2 i ^ - B 0 x x 2 + y 2 1 2 j ^ . Find current enclosed in the loop x 2 + y 2 = r 2. (1) B 0 r µ 0 (2) 2 B 0 r µ 0 (3) 2 π B 0 r µ 0 (4) B 0 r 2 µ 0