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4. A long line charge A (charge per unit length) is located at axis of a toroidal coil of rectangular cross section, as shown in Fig. 4. The inner radius of the coil is a, outer radius a+w, and height h, which carries a total of N tightly-wound turns and current /. (a) Find the electromagnetic momentum p of this configuration. Figure 4 0 a W h (b) Now the current in the toroid is turned off, quickly enough that the line charge does not move appreciably as the magnetic field drops to zero. Find the induced electric field at the center of the toroid. Here, you can assume that w and h are both much less than a.

4. A long line charge A (charge per unit length) is located at axis of a toroidal coil of rectangular cross section, as shown in Fig. 4. The inner radius of the coil is a, outer radius a+w, and height h, which carries a total of N tightly-wound turns and current /. (a) Find the electromagnetic momentum p of this configuration. Figure 4 0 a W h (b) Now the current in the toroid is turned off, quickly enough that the line charge does not move appreciably as the magnetic field drops to zero. Find the induced electric field at the center of the toroid. Here, you can assume that w and h are both much less than a.

Question
4. A long line charge A (charge per unit length) is located at axis of a toroidal coil of rectangular cross section, as shown in Fig. 4. The inner radius of the coil is a, outer radius a + w, and height h, which carries a total of N tightly-wound turns and current I. (a) Find the electromagnetic momentum p of this configuration. Figure 4 (b) Now the current in the toroid is turned off, quickly enough that the line charge does not move appreciably as the magnetic field drops to zero. Find the induced electric field at the center of the toroid. Here, you can assume that w and h are both much less than a. Hint: to find the induced electric field exploit the analogy between Faraday (induced) electric fields and magnetostatic fields of a circular current loop.
Transcribed Image Text:4. A long line charge A (charge per unit length) is located at axis of a toroidal coil of rectangular cross section, as shown in Fig. 4. The inner radius of the coil is a, outer radius a + w, and height h, which carries a total of N tightly-wound turns and current I. (a) Find the electromagnetic momentum p of this configuration. Figure 4 (b) Now the current in the toroid is turned off, quickly enough that the line charge does not move appreciably as the magnetic field drops to zero. Find the induced electric field at the center of the toroid. Here, you can assume that w and h are both much less than a. Hint: to find the induced electric field exploit the analogy between Faraday (induced) electric fields and magnetostatic fields of a circular current loop.
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