전자기학 중간고사 문제 (2022-4-21, 14:00-14:40)

학번 ( ) 성명 ( ) 이동전화번호( )

PIN = abcd: 학생의 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)

1. A = (a, b, c), B = (d, c, b). Find C = A×B

2. A = (a, b, c), B = (d, c, b). Find the angle (deg.) between A and B.

3. P = (x, y, z) = (b, c, d). Express P = (r, θ, φ) in the spherical coordinate system.

4. Write down an equation for a voltage wave traveling in +z direction with the following parameters.

amplitude = a (V)

frequency = b (MHz)

wavelength = c (m)

phase = d (rad)

5. A point charge Q = d×10⁻⁹ C at a point A = (d, a, b) (m). Find the electric field E (V/m) at a point B = (c, b, a) (m).

6. There are three point charges

Q₁ = a×10⁻⁹ C at a point P₁ = (b, c, d) m.

Q₂ = b×10⁻⁹ C at a point P₂ = (c, d, a) m.

Q₃ = c×10⁻⁹ C at a point P₃ = (d, a, b) m.

and a spherical surface S enclosing all the three charges. Find the total electric flux going throgh the spherical surface S.

7. A cylindrica resistor with cross sectin S = a (m²), length L = b (m), conductivity = c×10³ (S/m) with an applied voltage V = d (V) between end faces of the resistor. Find the resistance R (ohm) of the resistor, current density J (A/m2) in the resistor, and electric field E (V/m) in the resistor.

8. Two point charges at

Q₁ = a×10⁻⁹ C at a point P₁ = (b, c, d) m.

Q₂ = b×10⁻⁹ C at a point P₂ = (c, d, a) m.

Find the energy W (J) stored in the electric field.