Three particles having the same mass and the same horizontal velocity enter a re

Question

Three particles having the same mass and the same horizontal velocity enter a region of constant magnetic field. One particle has a charge q, the other has a charge -4 q and the third particle is neutral. The paths of the particles are shown in(Figure 1) .

Part A

In which direction does the magnetic field point?

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Figure 1 of 1

Three particles having the same mass and the same horizontal velocity enter a region of constant magnetic field. One particle has a charge q, the other has a charge -4 q and the third particle is neutral. The paths of the particles are shown in(Figure 1) .

Part A

In which direction does the magnetic field point?

In which direction does the magnetic field point? out of the screen into the screen downward upward

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Figure 1 of 1

Explanation / Answer

If you observe, you can find that out of the two deflected particles, the lower one has a bigger radius of curvature.

So the upper particle should have experienced a greater force to have been deflected so sharply when compared to the lower one and we know that the magnitude of the force os directly proportional to the charge. F = Q (VxB)

So, we conclude that the upper deflected particle has a charge -4q and the lower particle has a charge q.

Now the direction of force is given by the right hand rule. That is, when you curl your right hand fingers from V direction to B direction, your thumb gives the direction ot the force.

Hence if the Magnetic field is "INTO THE SCREEN", then the Force as the upper particle just enters the Magnetic field should have been -4qvB in the upward direction (apply right hand rule for cross product VxB) But, DO NOT FORGET THE NEGATIVE SIGN. That is the - ve sign in the term -4qvB tells us that the actual force acts in the direction opposite to that given by cross product of VxB.which mean the force would have acted downwards if the Magnetic field was into the screen. But, we see that the upper particle (-4q) has been deflected upwards. By which, it means that the Magnetic field is OUT OF THE SCREEN. Now apply right hand rule for VxB, assuming B is coming OUT OF THE SCREEN. You will find that the resultant of the cross product will point downwards. And after taking the -ve sign of -4qvB into consideration, the final Force would point upwards, which perfectly fits our explanation.

SO, ANSWER : OUT OF THE SCREEN

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