複選題
15. Which of the following are correct?

(A)There can be no electric field inside a solid conducting sphere

(B)the Gauss's Theorem of magnetism suggests that no magnetic monopole exists

(C)electric current flowing in a wire will produce a magnetic field

(D)a static magnetic field threaded through a loop will cause an emf

(E)alternately changing electric and magnetic fields will generate an electromagnetic wave

1. Two forces, \( F_1 \) and \( F_2 \), act on a particle with a mass of 1 kg and make it accelerate at \( 4\hat{i} - 6\hat{j} + 2\hat{k} \) (m/s²). If \( F_1 = -2\hat{i} + \hat{j} + 5\hat{k} \) (N), find \( F_2 \). (A)\( 2\hat{i} - 7\hat{j} - 3\hat{k} \) (N) (B)\( 2\hat{i} - 5\hat{j} + 5\hat{k} \) (N) (C)\( F_2 = 6\hat{i} - 5\hat{j} + 5\hat{k} \) (N) (D)\( F_2 = 6\hat{i} - 7\hat{j} - 3\hat{k} \) (N) (E)\( F_2 = 2\hat{i} - 5\hat{j} \) (N)

2. A particle moves along the x-axis according to the equation \( 5t = 3x^2 + 4x + 6 \), where x is the position in meter and t is the time in second. Find its speed when \( x = 1.0 \) m. (A)2.0 (B)1.5 (C)1 (D)0.5 (E)0.1 (m/s)

3. Which of the following does not represent the dimension of force? (m: mass, x: position, v: speed, a: acceleration, k: force constant, q: charge, E: electric field, B: magnetic induction) (A)ma (B)kx (C)qE (D)qB (E)\( mv^2/x \)

4. A solid wheel with mass M, radius R, rolls without sliding on a horizontal surface and its rotational inertia is \( MR^2/2 \). If the center of mass is accelerating at a. Find the applied force F acting on the axle and the frictional force f on the wheel surface. (F, f) = (A)(Ma, 0) (B)(Ma, Ma/2) (C)(2Ma, Ma) (D)(2Ma, Ma/2) (E)(3Ma/2, Ma/2)

5. A wheel takes 3.00 s to rotate 36.0 rounds. Its angular speed at the end of the 3.00-s interval is 27.0 rad/s. What is the constant angular acceleration of the wheel? (A)2.0 (B)1.0 (C)3.0 (D)0.5 (E)4.0 (rad·s⁻²)

6. A charge of 10 C is first put on a spherical conducting shell and then another point charge of -3 C is put at the center. Find the net charge on the outer surface of the shell: (A)-7 C (B)-3 C (C)0 C (D)+3 C (E)+7 C

7. A capacitor of capacitance C and an inductor of inductance L are connected on both ends, the resonance angular frequency is: (A)LC (B)\( (LC)^{1/2} \) (C)\( (LC)^2 \) (D)\( (1/LC)^{1/2} \) (E)L/C

8. A magnetic field B passing in perpendicular through a square wire loop of area A. The magnetic flux through the loop is: (A)0 (B)BA/2 (C)BA (D)2BA (E)3BA

9. In the right figure, \( R_1 = 5\Omega \), \( R_2 = 10\Omega \), \( R_3 = 15\Omega \), \( C_1 = 5\mu F \), \( C_2 = 10\mu F \), and the ideal battery has an emf \( \varepsilon = 20V \). In steady state, the total energy stored in the two capacitors is: (A)\( 2.78\times10^{-5} \) J (B)\( 1.12\times10^{-4} \) J (C)\( 2.22\times10^{-4} \) J (D)\( 2.50\times10^{-4} \) J (E)\( 4.72\times10^{-4} \) J

10. A monochromatic light (\( \lambda = 560 \) nm) is incident on a thin film with refractive index n = 1.40. How thick must the film be in order for destructive interference to occur when reflected? (A)100 nm (B)200 nm (C)150 nm (D)250 nm (E)50 nm

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