A long cylindrical wire centered at x = 0 cm and y = 0 cm has a hole through the

Question

A long cylindrical wire centered at x = 0 cm and y = 0 cm has a hole through the center, throughout its entire length as shown in the figure. The radius of the wire is sigma = 2.00 cm. The radius of the hole is 0.500 cm. Assume a uniform current density with magnitude I_0 = 16.0 A/m^2 runs into the page. Consider three circular Amperian loops drawn in the diagram, A (dashed line), B(dotted line), and C(dash-dotted line). The radii of these Amperian loops are r = 0.400 cm, r = 1.75 cm, and r = 2.50 cm respectively. What is the of magnitude of the B field along Amperian loop A? What is the magnitude of the B field along the Amperian loop B? What is the magnitude of the B field along Amperian loop C? Draw the B field along Amperian loop C on the figure. The hole in the wire is now filled in so that the wire is entirely solid. Assume the current density now varies as J(r) = J_0 (t - r/k), where k = 3.00 cm. What is the magnitude of the B field along Amperian loop C now? Loop A: r_a = 0.40 cm Loop B: r_b = 1.75 Loop C: r_c = 2.50 cm

Explanation / Answer

A) B = 0 as current enclosed is zero

b) B = uoi/[2pi r]

= 2e-7*16*pi*0.0175^2/0.0175

= 1.76*10^-7 T

c) B = uoi/[2pi r]

= 2e-7*16*pi*0.02^2/0.025

= 1.61*10^-7 T

d) Direction at c, will be in clockwise direction along that circular surface.

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