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  4. A uniform magnetic field acts right angles to the direction of motion of electrons. As a result, the electron moves in a circular path of radius 2 cm. If the speed of electrons is doubled, then the radius of the circular path will be

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Q. A uniform magnetic field acts right angles to the direction of motion of electrons. As a result, the electron moves in a circular path of radius $2 \,cm$. If the speed of electrons is doubled, then the radius of the circular path will be

AIPMTAIPMT 1991Moving Charges and Magnetism

Solution:

$r=\frac{m v}{q B}$ or $r \propto v$
As $v$ is doubled, the radius also becomes doubled.
Hence radius $=2 \times 2=4 cm$.