Question

the magnitude of velocities of two alpha particles A and B entering a uniform magnetic field perpendicularly, are in the ratio 6:1. on entering the field , they move in circular paths. find out the ratio of radii of their paths.
solve it by giving proper explaination about the formula.

Answer 1

Question #54316, Physics / Electromagnetism

the magnitude of velocities of two alpha particles A and B entering a uniform magnetic field perpendicularly, are in the ratio 6:1. on entering the field, they move in circular paths. find out the ratio of radii of their paths.

solve it by giving proper explanation about the formula.

Answer:

The force exerting on the charged particles moving in the magnetic field is defined by the equation:

$$F = qvB$$

, where $q$ – the charge, $v$ – the velocity and $B$ – the magnetic field

At the same time the centripetal force acting on the object is:

$$F_c = (mv^2)/r$$

Since these forces have the same magnitude the final equation should be:

$$qvB = (mv^2)/r,$$ $$r = (mv)/(qB)$$

Therefore for particles having the same mass and charge, which are travelling in the same magnetic field, their radii are proportional to their velocities:

For alpha particle A: $r(A) = [m/(qB)] \cdot v(A)$

For alpha particle B: $r(B) = [m/(qB)] \cdot v(B)$

$$r(A)/r(B) = \frac{v(A)}{v(B)} = \frac{6}{1} = 6$$

The radius of trajectory for A is in 6 times larger than that for B.

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