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A solid cylindrical conducting shell of inner radius a = 4.4 cm and outer radius b = 6.3 cm has its axis aligned with the z-axis as shown. It carries a uniformly distributed current I2 = 7.5 A in the positive z-direction. An inifinte conducting wire is located along the z-axis and carries a current I1 = 2.2 A in the negative z-direction.

1) What is By(P), the y-component of the magnetic field at point P, located a distance d = 32 cm from the origin along the x-axis as shown?

33.125 *10^-7 T

2) What is

∫PSB⃗ ⋅dl⃗

where the integral is taken along the dotted path shown in the figure above: first from point P to point R at (x,y) = (0.707d, 0.707d), and then to point S at (x,y) = (0.6d, 0.6d).

8.325*10^-7 T-m

3) What is By(T), the y-component of the magnetic field at point T, located at (x,y) = (-5.1 cm,0), as shown?

-9.932*10^-7 T

4)What is

∫SPB⃗ ⋅dl⃗

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

-8.325*10^-7 T-m

5) Suppose the magnitude of the current I2 is now doubled. How does the magnitude of the magnetic field at (x,y) = (2.2 cm, 0) change?

B(2.2 cm, 0) remains the same

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