전자기학 기말고사 문제 (2021-6-7, 16:00-14:40)

학번 ( ) 성명 ( ) 이동전화번호( )

PIN = abcd: 휴대전화 끝 4 자리 (예: 010-8028-3194, a = 3, b = 1, c = 9, d = 4), 단 각 숫자가 0인 경우 순차적으로 1, 2, 3, 4로 대체 (예: 010-1234-0097인 경우 a = 1, b = 2, c = 9, d = 7)

참고 a_y: unit vector in +y direction.

1. A a (C) charge is moving with a velocity of u = ba_y + ca_z (m) in a magnetic flux density B = 3a_x + da_z (T), find the force F (N) on the charge.

2. A current of d (A) flows along the z axis in a_z direction in vacuum. Find the magnetic field H at (x, y, z) = (c, b, a) m.

3. The magnetic vector potential function is given by A(x, y, z) = (c xy + d y + a zy + b) a_z (Wb/m). Find the magnetic flux density function B(x, y, z) (Wb/m²).

4. The plane z = 0 is the boundary between the air and a magnetic material with relative permeability of a. In the air, H = (H_x, H_y, H_z) = (b, d, c) (A/m). Find the B (T) in the magnetic material.

5. N = 100a, find 1) the reluctance R and 2) the magnetic flux Φ (Wb) in the core. The core material is the electrical steel with relative permeability of 1000b. The core's cross section is a square. The applied current is I = b (A). The core dimensions are h = 10d (cm), l = c (cm), w = d (cm).

6. Magnetic field in air is given by H = a sin(ct + π) a_z (A/m). A d-turn (N = d) conducting loop of radius r = b m is placed on the xy plane. Find the voltage V_m induced in the loop.

7. Given E(z, t) = ba_xcos(2aπ×10⁹t − kz), ε = cε₀, μ = dμ₀ in a source-free region, find 1) the wavelength λ (m) and 2) H(z, t) (A/m).