Question

An electron is moving in a uniform magnetic field B in a circular orbit of radius r. Suddenly the field is reduced to B/2.The radius of the path now becomes (1)2r (2)r/2 (3)r (4)4r

Answer 1

Question #74559, Physics / Electromagnetism

An electron is moving in a uniform magnetic field B in a circular orbit of radius r. Suddenly the field is reduced to B/2. The radius of the path now becomes (1)2r (2)r/2 (3)r (4)4r

Need to find $-r_{I}$

Solution:

Lorentz force $F_{L} = e v B$ , from picture can be seen, that $F_{L} = F_{c}$ .

Then, $m\frac{v^2}{r} = evB \rightarrow r = \frac{mv}{eB}$ . If $B_1 = \frac{1}{2} B \rightarrow r_1 = \frac{mv}{e_2^B} = 2\frac{mv}{eB} \rightarrow r_1 = 2r$ .

Answer: (1) - 2r.

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