Question

A solid cylindrical conducting shell of inner radius a = 4.9 cm and outer radius b = 6 cm has its axis aligned with the z-axis as shown. It carries a uniformly distributed current I₂ = 5.8 A in the positive z-direction. An inifinte conducting wire is located along the z-axis and carries a current I₁ = 3.8 A in the negative z-direction.

$h15_cylinders$

1. What is B_y(T), the y-component of the magnetic field at point T, located at (x,y) = (-5.3 cm,0), as shown?

2. What is

$\int_{s}^{p}$ B⃗ ⋅dl⃗

where the integral is taken on the straight line path from point S to point P as shown?

$h15_cylindersD$

Answer 1

The ratio of the enclosed current and current in the circuit is 12-a 2 ,enc (0.0532 -0.0492 0.062-0.053 (5.8) 299 A The total current is enc enic --3.8+2.99 -0.81 A The y component magnetic field is t101 enc 2Td 4x100.81) (2T (-0.053) -3.06x10-6 T The ends point of the path PR and SR are same since the line integral of the magnetic field strength of the path SR also must be the same as PR but will have negative sign Therefore the line integral of the magnetic field along the path SR