JEE Mains · Physics · STD 12 - 4. Moving charges and magnetism

The figure shows a region of length \('l'\) with a uniform magnetic field of \(0.3\, T\) in it and a proton entering the region with velocity \(4 \times 10^{5}\, ms ^{-1}\) making an angle \(60^{\circ}\) with the field. If the proton completes \(10\) revolution by the time it cross the region shown, \(l\) is close to....... \(m\) (mass of proton \(=1.67 \times 10^{-27} \,kg ,\) charge of the proton \(\left.=1.6 \times 10^{-19}\, C \right)\)

A \(0.11\)
B \(0.22\)
C \(0.44\)
D \(0.88\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(0.44\)

Step-by-step Solution

Detailed explanation

\(T =\frac{2 \pi m }{ qB }\) total time \(t=10 T\) Kinematics \(\ell=\frac{ V }{2} t\) \(\ell=\frac{V}{2} 10 \times \frac{2 \pi m}{q B}\) \(=4 \times 10^{5} \times 10 \times \frac{3.14 \times 1.67 \times 1 0^{-27}}{1.6 \times 10^{-19} \times 0.3}\) \(=0.439\)

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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	List-I		List-II
A.	Magnetic induction	I.	\(M L T ^{-2} A^{-2}\)
B.	Magnetic flux	II.	\(ML ^2 T^{-2} A^{-2}\)
C.	Magnetic permeability	III.	\(ML ^0 T^{-2} A^{-1}\)
D.	Self inductance	IV.	\(ML ^2 T^{-2} A^{-1}\)