Question

A solid cylindrical conducting shell of inner radius a -4 cm and outer radius b 6.7 cm has its axis aligned with the z axis as shown. It carries a uniformly distributed current l2- 7.8 A in the positive z-direction. An inifinte conducting wire is located along the z-axis and carries a current i1 = 3.6 A in the negative z-direction. , R(7074, 707d) R(7074.7074) Pido) 1) What is By(P), the y-component of the magnetic field at point P, located a distance d- 22 cm from the origin along the x-axis as shown? T Submit

Answer 1

1 )

B = $\mu$ ₀ i / 2 $\pi$ d

i = i₂ - i₁

i = 7.8 - 3.6

i = 4.2 A

B_y(P) = 4 X 3.14 X 10^-7 X 4.2 / 2 X 3.14 X 0.21

B_y(P) = 4 X 10^-6 T

2 )

$\tiny \int_{P}^{S}$ B .d L = B X 3.14 X 0.21 / 4

$\tiny \int_{P}^{S}$ B .d L = 4 X 10^-6 X 3.14 X 0.21 / 4

$\tiny \int_{P}^{S}$ B .d L = 6.59 X 10^-7 T . m

3 )

i_2,enc = i₂ ( 3.14 ( r² - a² ) / 3.14 ( b² - a² ) )

i_2,enc = 7.8 X ( ( 4.6² - 4² ) / ( 6.7² - 4² ))

i_2,enc = 1.39

i_enc = i₁ + i_2,enc

i_enc = -3.6 + 1.39

i_enc = -2.21 A

B_y(T) = - 4 X 3.14 X 10^-7 X ( -2.21) / 2 X 3.14 X 0.046 )

B_y(T) = 9.6 X 10^-6 T

4 )

$\tiny \int_{S}^{P}$ B .d L = - 6.59 X 10^-7 T . m

( same way limits are changed )

5 )

B ( 2 cm , 0 ) remains the same