Consider the seven current-carrying wires and the four closed paths shown in the

Question

Consider the seven current-carrying wires and the four closed paths shown in the figure. For each of these paths (C_1, C_2, C_3, and C_4) determine the following in terms of mu_0. Use standard sign convention for the currents; minus is down into the page and positive is up out of the page. (Assume I_1 = 5.00 A, I_2 = 4.00 A, I_3 = 4.00 A, I_4 = 4.00 A, I_5 = 9.00 A, I_6 = 6.00 A, and I_7 = 7.00 A.) ContourIntegral_c_1 B^rightarrow middot ds^rightarrow = (____________A)mu_0 ContourIntegral_c_2 B^rightarrow middot ds^rightarrow = (____________A)mu_0 ContourIntegral_c_3 B^rightarrow middot ds^rightarrow = (____________A)mu_0 ContourIntegral_c_4 B^rightarrow middot ds^rightarrow = (____________A)mu_0

Explanation / Answer

B.ds = uo*Ienc

part a )

c1 enclosed I1 = out of the page

B.ds = 5 uo

part b )

c2 enclosed I1 and I3 , I3 is into the page

Ienc= I1 - I3 = 5 -4 = 1 A

B.ds = 1A*uo

part c )

c3 enclosed I1 , I2 and I3 where I1 is out of the page , I2 and I3 into page

Ienc = I1 - I2 - I3 = 5 -4 -4 = -3 A

B.ds = -3Auo

part d )

c4 includes I1 , I2 , I3 and I4 where I1 and I4 out of the page and I2 , I3 into the page

Ienc = I1 + I4 - I2 - I3 = 1 A

B.ds = 1A*uo

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