8. A rectangular conducting loop of length a and width b is placed at a distance L away from a very long straight wire that carries a constant current Io, see Fig. 8. The long wire current produces a (non-uniform) magnetic field in the space around it: B(x) =- Holo with x being the distance of a point away from the long wire current. (a). Determine the magnetic flux through the rectangular loop. [hint: decompose the loop into many narrow band and then use integration] (b). If the rectangular loop is pulled away from the long wire current at constant speed v (so L is dL increasing and v=), what emf ɛ is induced in the loop? dt (c). If the total resistance of the rectangular loop is R, determine the induced current flowing in the loop. Does the induced current flow clockwise or counter-clockwise? (d). Determine the force F required to pull the loop away. ва Fig.8 for Problem 8.

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3. Follow the above problem No. 1 Fig. (b). Two negative charges, gi and ga, move into the magnetic field with the same velocity. gi has mass mi, while q2 has mass m2. I that gi 3qs and mi 2/3. Which one of the following answers is correct, about their radi, ri and T2 of their circular motions? (a) T1/T2 = 1, (b) n/n , (c) n/r2-1/9, (d) r1/ 1/3, and () n/r2-3.

(a) What is the maximum torque on a 181-turn square loop of wire 18.0 cm on a side that carries a 38.0-A current in a 1.60-T field? N. m (b) What is the torque when o is 20.0°? N.m