An electron having charge 1.6×10-19 C and mass 9×10-31 kg is moving with 4×106 m s-1 speed in a magnetic field 2×10-1 T in a circular orbit. The force acting on electron and the radius of the circular orbit is _____

AP EAMCET · PHYSICS · Magnetic Effects of Current

An electron having charge $1.6 \times 10^{- 19} C$ and mass $9 \times 10^{- 31} kg$ is moving with $4 \times 10^{6} m s^{- 1}$ speed in a magnetic field $2 \times 10^{- 1} T$ in a circular orbit. The force acting on electron and the radius of the circular orbit is _____

A $12.8 \times 10^{- 13} N, 1.1 \times 10^{- 4} m$
B $1.28 \times 10^{- 14} N, 1.1 \times 10^{- 3} m$
C $1.28 \times 10^{- 13} N, 1.1 \times 10^{- 3} m$
D $1.28 \times 10^{- 13} N, 1.1 \times 10^{- 4} m$

Verified Solution

Answer & Solution

Correct Answer

(D) $1.28 \times 10^{- 13} N, 1.1 \times 10^{- 4} m$

Step-by-step Solution

Detailed explanation

Force due to magnetic field on moving charge is given by F=qvB ⇒F=1.6×10-19×4×106×2×10-1=1.28×10-3 N Radius of circular path F=mv2r ⇒r=mv2F=9×10-31×4×10621.28×10-13=1.1×10-4 m

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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