18. The mass spectrometer. In 1910, W. Aston proposed and constructed an experiment measuring the mass of a charged particle. The key elements of a mass spectrometer are shown in Figure 4. A collimated beam enters the velocity selector. Upon emerging from slit C, these particles of velocity u now enter a region with only a magnetic induction B₀perpendicular to the plane of the diagram. These particles experiencing the Lorentz force traverse a semicircular path (with radius R) until they strike a screen. Find the resulting radius R . 
(A)
(B)
(C)
(D)

複選題1. Newton's law of gravitation states that there exists an attractive force between the planet and the sun of masses m and M, respectively. The magnitude of the force is written as F = GmM /r2, where r is the distance of the planet from the sun, which is called the central force. The orbital motion of a particle under a central force is always (A)unbounded (B) bounded (C) confined to a plane (D) None of these.

2. Hook's law of spring states that if you stretch a spring from its equilibrium length by a displacement x, then the force F that the spring exerts on you is F = -c . Now a particle of mass m is executing oscillation obeying Hook's law. If the amplitude of oscillation is A, then its period is (A)proportional to (B) independent of A (C) proportional to 1/ (D) proportional to A2.

3. Experiments show that any liquid is incompressible. This implies that the density of a liquid (A) is a constant (B) varies at different parts of liquid (C) behaves like a gas (D) None of these.

4. When a charged particle (charge q and mass m) moves with velocity u through a region of space where both electric field E and magnetic induction field B are present. The charged particle would experience a force F. In vector form, the force is (A) F=qE+uxB (B) F=qExB (C) F=qu(E.B) (D) F=q(E+uxB) .

5. Two conducting plates have an area A and are separated by a distance d. The capacitance C of the parallel-plate capacitor is (A)(B)(C) (D) , where ε0, is the electric constant and μ0is the magnetic constant in a vacuum.

6.A very long ideal solenoid with a cross-section area A has N turns and a length l . Assume that each turn is circular. The self-inductance Ls of this ideal solenoid is NA (A) (B)(C) (D) , where ε0 is the electric constant and μ0 is the magnetic constant in a vacuum.

7.The classic method used to demonstrate the essential features of interference of light was devised by Thomas Young, namely, Young's two-slit experiment. The distance between any two consecutive bright fringes (or dark fringes) is called fringe width. Now if the whole Young's two-slit apparatus is immersed in water, the fringe width will (A) increase (B) decrease (C) unchanged (D) disappear. N-uA

8. The unit of magnetic induction field B is denoted as [B]=[N]/[A.m] and the electric field is [E]=[V] /[m], where [N] is Newton, [A] Ampere [V] Volt, and [m] meter. The clectric field due to an infinite non-conducting plane with uniform surface charge densityσ is given by E=σ /2ε0, where ε0 is the electric constant. On the other hand, the magnetic induction inside an ideal solenoid with steady current I is given by B= μ0nl , where  μ0 is the magnetic constant and n is the number of turns per unit length. By using these hints, the quantity has the dimension of (A)pressure (B) charge current (C) angular momentum (D) resistance.

9. The total energy E= K +V of a particle traveling under the conservative force field is a constant of motion, where K is the kinetic energy and V is the potential energy. In a one-dimensional case, say the x-axis, the conservative force is related to potential energy by which equation? (A) (B) (C) (D)

10. A planet of mass m orbits the sun of mass M in an elliptical path (see Figure 1), with the sun at a focal point. In accord with Kepler's laws, a line drawn from the sun to a planet sweeps out equal areas in cqual times, i.e., dAidt is a constant. Assume that the angular momentum of the planet relative to the sun is L, then dA/ dt is given by  (A) (B) (C) (D)

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