A charged particle enters a region which offers a resistance against its motion and a uniform mangetic field exists in the region. The particle traces a spiral path as shown in Fig. 1.29. State the following statements as True or False.
a. Component of magnetic field in the plane of spiral is zero.
(b) Particle enters the region at Q.
If magnetic field is outwards, then the particle is positively charged.
(d) If magnetic field is outwards, then the particle is negatively charged.

Explanation

(a) True, (b) True, (c) False, (d) True
Force exerted by the magnetic field is in the plane of spiral.
Direction of magnetic field is always normal to both the velocity
vector and direction of force. It means magnetic field is normal
to plane of the spiral. Hence (a) is correct.
Since the particle expreriences a resistance against its motion,
therefore, its speed decrease continuously. Radius fo the cir-
cular path followed by a charged particle moving in a magnetic
field is given by `R=mv//qB`. Since v is continuously. Hence, a charged
particle should follow a spiral path of decreasing radius. Hence,
the particle enters the magnetic field at Q. Hence (b) correct.
For the given spiral, force should act as
shown. if v and B are as shown in Fig.
then F can be in the shown direction
only for a negative charge. Hence (c) is
false, (d) is true.