In a microwave oven, the electric field does most of the work, but there are cas

Question

In a microwave oven, the electric field does most of the work, but there are cases in which the magnetic field causes dramatic effects. If you put a mug with a gold rim around the top in in a microwave oven, the changing magnetic field inside the loop generates a large emf, and the small resistance means a large current. Sparks will fly! If the intensity of the microwaves is 5000 W/m^2 and the frequency is 2.4 GHz and the diameter of the mug is 8.0 cm, a. Compute the magnitude of the magnetic field. b. Compute the change in field as the wave goes from its maximum positive value to its maximum negative value. c. Compute the change in flux corresponding to this field change. d. If the gold rim has a resistance of 0.20 Ohm, what is the current? (You'll get a large number here; the actual current will be less than this due to other effects.)

Explanation / Answer

(A) I = c Bm^2 / 2 u0

5000 = (3 x 10^8) Bm^2 / (2 x 4pi x 10^-7)

Bm = 6.472 x 10^-6 T

(B) change in field = 2 Bm = 12.94 x 10^-6 T

(c) change in flux = (pi 0.04^2) (12.94 x 10^-6) = 6.506 x 10^-8 Wb

(d) e = N A B w

= 6.506 x 10^-8 x (2 x pi x 2.4 x 10^9)

= 981 Volt

I = e / R = 4905.75 A

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