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Question

# A charged particle moving in a uniform magnetic field when losses 4% of its kinetic energy, the radius of curvature of its circular path:

A
Decreases by 2%
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B
Increases by 2%
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C
Increases by 4%
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D
Decreases by 4%
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Solution

## The correct option is A Decreases by 2%We know the radius of a circular path of charge q moving with kinetic energy K in a uniform magnetic field is given by, r=√2mKqB As m, q and B are the same for the same charge. ∴r ∝√K r=CK12 (where, C is a constant) Taking log on both sides, we get logr=logC+12logK Differentiating both sides; 1r×dr=0+12(1K)dK drr×100=12×dKK×100 As given, dKK×100=4% ∴drr×100=12×4=2% Thus, radius will be decreasing by 2%. Hence, option (a) is the correct answer.

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