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Sol_Quiz1

# Sol_Quiz1 - I max = 35 μA(b the value of V Solution ω = 2...

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PHYS 4D Solution to Quiz 1 January 14, 2011 Problem 1 Electromagnetic waves and sound waves can have the same frequency. (a) What is the wavelength of a 1 KHz electromagnetic wave? Solution: λ = c/f = (3 . 0 × 10 8 m/s ) / (1 × 10 3 /s ) = 3 × 10 5 m. (b) What is the wavelength of a 1 KHz sound wave? ( v sound = 341 m/s ) Solution: λ = v sound /f = (341 m/s ) / (1 × 10 3 /s ) = 0 . 341 m. Problem 2 An electromagnetic wave has a magnetic field given by B = i B 0 cos ( kz - ωt ) , where B 0 = 1 . 5 × 10 - 4 T, k = 10 - 3 m - 1 and ω = 3 × 10 5 rad/s. (a) Write down an expression for the electric field. Solution: The directions of E , B , k obey ˆ E × ˆ B = ˆ k . Now, ˆ B = i , ˆ k = z ˆ E = - j . E 0 = cB 0 = 4 . 5 × 10 4 V/m. E = - j E 0 cos ( kz - ωt ) , (b) What are the wave length and frequency of the wave? Solution: λ = 2 π k = 6 . 3 × 10 3 m, f = ω 2 π = 4 . 8 × 10 4 Hz. Problem 3 An air-gap capacitor has circular plates of radius k = 2 . 5 cm and separation d = 1 . 6 mm . A 76 . 0 Hz emf V = V 0 cos ωt is applied to the capacitor. The maximum displacement current is 35 μA. Determine (a) the maximum conduction current I ; Solution: The footnote on page 816 indicates that Kirchhoff’s junction rule is valid at a capacitor plate, and so the conduction current is the same as the displacement current. Thus

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Unformatted text preview: I max = 35 μA . (b) the value of V ; Solution: ω = 2 πf = 4 . 78 × 10 2 rad/s 1 I = dQ dt = C dV dt =-CωV sin ωt, I max = CωV ,C = ε A d . ⇒ V = I max Cω = I max d ωε A = 6 . 75 × 10 3 V (c) the maximum value of d Φ E /dt between plates. Solution: I D = ε d Φ E dt ⇒ ( d Φ E dt ) max = I max ε = 3 . 95 × 10 6 V · m/s. Bonus Problem A 1500-nF capacitor with circular parallel plates 2 cm in diameter is accumulating charge at the rate 38 mC/s at some instant in time. (a) What will be the induced magnetic ﬁeld strength 10 cm radially outward from the center of the plates? Solution: B (2 πr ) = μ I. B = μ I 2 πr = 7 . 6 × 10-8 T (b) What will be the value of the ﬁeld strength after the capacitor is fully charged? Solution: Since I = 0 , B = 0 . 2...
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Sol_Quiz1 - I max = 35 μA(b the value of V Solution ω = 2...

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