This is a two part questuion I have a hard time understanding this chapter, if y

Question

This is a two part questuion
I have a hard time understanding this chapter, if you could explain the reason behind the answer that would be great, thank you

+0 A particle of electric charge +0 and mass m initially moves along a straight line in the plane of the page with constant speed v, as shown above. The particle enters a uniform magnetic fieid of magnitude B directed out of the page and moves in a semicircular arc of radius R. Which of the following best indicates the magnitude and the direction of the magnetic force F on the charge just after the charge enters the magnetic field? 7. Magnitude ko Direction (A) A Toward the top of the page Toward the bottom of the page R2 (c) OvB Out of the piane of the page Toward the top of the page Toward the bottom of the page 8. If the magnetic field strength is increased, which of the following will be true about the radius R? L R increases if the incident speed is held constant. IL. For R to remain constant, the incident speed must be increased. ?1. For R to remain constant, the incident speed must be decreased. (A) I only (B) 11 only (c) III only (D) I and II only () I and III only

Explanation / Answer

7. The lorentz force on a charged particle moving with velocity v in a magnetic field B is given by,

F = Q(v x B) [cross product of vectors]

As v has direction right ways and B has direction out of the paper , both perpendicular to each other, v x B has direction out of the paper and magnitude of v x B is vB.

Hence, force F = QvB out of the plane of paper.

8. As B increases, the force QvB increases, which makes the particle move in smaller circles. To increase the radius of gyration, which is given by:

R = mv/QB

v must be increased in accordance with B, so that R must remain constant.

(B) Only (II) is the correct option.

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