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題組內容

4. Two semicircular loops of radii a and b have a common center and their ends are joined by straight wires, as shown in Fig. 4.

(b) Find the magnetic moment of the loop? (5 %)

其他申論題

(a) Find the flux of B through the loop. (15 %)

(b) If someone now pulls the loop directly away from the wire, at speed v，what electromotive force is generated? In what direction does the current flow? (12 %)

(c) What if the loop is pulled to the right at speed v，instead of away? (Give the reasons for your answer.) (3 %)

(a) What is the resultant magnetic field at the center? (20 %)

(b) The null spaces of T and U are finite-dimensionai. Then the null space of TU is finite-dimensional, and dim(N(TU)) = dzm(N(T)) + dim(N(V)).

【已刪除】20% 2. Show that if W is a finite-dimensional subspace of an inner product space V. Then

(a) Find the orthonormal basis 0 of (y1,y2,y3).

(b) Find the coefficients of x = (2，1,3) in the orthonormal basis β.

(1) Suppose that i4 is an 8 x 8 matrix, A - I has nullity 2，(A - I)2 has nullity 4, (A- I)k has nullity 5 for ≥ 3, and (A + 2)j has nullity 3 for j ≥ 1.

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