First slide

Force on a charged particle moving in a magnetic field

Question

Statement 1: When a charging particle is fired in a magnetic field, the radius of its circular path is directly proportional to the kinetic energy of the particle.
Statement 2: The centripetal force on the test charge q₀ is q₀v² B, where v is the velocity of a practical and B is the magnetic field in which the test charge in fired.

Moderate

A

Both statements 1 and 2 are correct
B

Statement 1 is correct statement 2 is incorrect
C

Statement 1 is incorrect statement 2 is correct
D

Both statements 1 and 2 are incorrect

Solution

If the path of the charged particle is circular, then radius of circular path is directly proportional to the speed and mass of the particle as $r = \frac{mv}{q_{0} B}$
$\begin{array}{l} ∴ Centripetal force = \frac{{mv}^{2}}{r} = q_{0} vB \\ Also, r = \sqrt{2 mK} / qB \end{array}$

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