Q.

A charged particle enters into a region which offers a resistance against its motion and  a uniform magnetic field exists in the region. The particle traces a planar spiral path as  shown in figure. Which of the following statement(s) is / are correct?

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a

If magnetic field is out of the page of the diagram, then the particle is negatively  charged 

b

Component of magnetic field in the plane of spiral is zero 

c

The particle enters the region at Q

d

If magnetic field is out of the page of the diagram, then the particle is positively  charged 

answer is A, B, C.

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Detailed Solution

A) WHENEVER A PARTICLE MOVES ALONG A SPIRAL PATH, ITS VELOCITY ALWAYS REAMINS IN THE PLANE OF SPIRAL OR THE COMPONENT OF THE VELOCITY NORMAL TO THE PLANE OF SPIRAL IS ALWAYS EQUAL TO ZERO. FORCE EXERTED BY MAGNETIC FIELD IS ALWAYS NORMAL TO THE DIRECTION OF MOTION OF THE PARTICLE.

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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 THE DIRECTION OF FORCE. IT MEANS, MAGNETIC FIELD IS NORMAL TO THE PLANE OF SPIRAL.
B) SINCE THE PARTICLE EXPERIENCES A RESISTANCE AGAINST ITS MOTION, THEREFORE ITS SPEED DECREASES CONTINUOUSLY. RADIUS OF THE CIRCULAR PATH FOLLOWED BY A CHARGED PARTICLE MOVING IN A MAGNETIC FIELD IS GIVEN BY 
R=mvqB Since v is continuously decreasing, therefore radius R also decreases continuously. So, a charge particle should follow a spiral path of decreasing radius. Hence, the particle enters the magnetic field at Q.
C) Force experienced by the particle is towards the center and direction of the force is found out by Fleming’s left hand rule. Since magnetic field is outward, therefore according to Fleming’s left hand rule, the direction of current associated with its motion should be as shown in figure. Since the particle is moving in the same direction, therefore the particle is positively charged.
D) Option (D) is not correct.

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