Motion of Charged Particle in Magnetic Field – Rankers Physics

Force Acting on Moving Charges: Practice Problem & Solution

Assertion (A): A charged particle is moving in a circle with constant speed in uniform magnetic field. If we increase the speed of particle to twice, its acceleration will become four times. Reason (R): A charge particle in circular path with constant speed in magnetic field, acceleration is given by centripetal acceleration. If speed is doubled centripetal acceleration will become four times.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Force Acting on Moving Charges. Understanding the underlying formula is key to arriving at the correct answer below:

The centripetal acceleration for a charged particle in a magnetic field is \( a = frac{qvB}{m} \). If speed \( v \) is doubled, then acceleration \( a \) will also double, not quadruple. So, Assertion (A) is false. Similarly, in this context, Reason (R) is also false. Thus, both are false.

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