Q: Calculate the torque exerted on the square loop shown in Fig.
Calculate the torque exerted on the square loop shown in Fig. 6.6, due to the circular loop (assume r is much larger than a or b). If the square loop is free to rotate, what will its equilibrium orien...
See AnswerQ: Calculate the line integral of the function / from
Calculate the line integral of the function / from the origin to the point (1,1,1) by three different routes: (a) (0, 0, 0) → (1, 0, 0) → (1, 1, 0) → (1, 1, 1). (b) (0, 0, 0) → (0, 0, 1) → (0, 1, 1)...
See AnswerQ: An iron rod of length L and square cross section (side
An iron rod of length L and square cross section (side a) is given a uniform longitudinal magnetization M, and then bent around into a circle with a narrow gap (width w), as shown in Fig. 6.14. Find t...
See AnswerQ: In Sect, 6.2.1, we began with
In Sect, 6.2.1, we began with the potential of a perfect dipole (Eq. 6.10), whereas in fact we are dealing with physical dipoles. Show, by the method of Sect. 4.2.3, that we nonetheless get the correc...
See AnswerQ: An infinitely long cylinder, of radius R, carries a “
An infinitely long cylinder, of radius R, carries a “frozen-in” magnetization, parallel to the axis, M = ks zˆ, where k is a constant and s is the distance from the axis; there is no free current anywh...
See AnswerQ: Suppose the field inside a large piece of magnetic material is B0
Suppose the ï¬eld inside a large piece of magnetic material is B0, so that H0 = (1/μ0)B0 − M, where M is a “frozen-inâ€...
See AnswerQ: For the bar magnet of Prob. 6.9, make
For the bar magnet of Prob. 6.9, make careful sketches of M, B, and H, assuming L is about 2a. Compare Prob. 4.17.
See AnswerQ: If J f=0 everywhere, the curl of H vanishes
If J f=0 everywhere, the curl of H vanishes (Eq. 6.19), and we can express H as the gradient of a scalar potential W : H = −∇W. According to Eq. 6.23, then, ∇2 W = (∇ · M), so W obeys Poisson’s equati...
See AnswerQ: A coaxial cable consists of two very long cylindrical tubes, separated
A coaxial cable consists of two very long cylindrical tubes, separated by linear insulating material of magnetic susceptibility χm . A current I flows down the inner conducto...
See AnswerQ: A current I flows down a long straight wire of radius a
A current I flows down a long straight wire of radius a. If the wire is made of linear material (copper, say, or aluminum) with susceptibility χm , and the current is distributed uniformly, what is the...
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