A charged particle carrying charge 1,μ C is moving with velocity (2 i +3 j +4 k), ms -1. If an external magnetic field of (5 i +3 j -6 k) × 10-3, T exists in the region where the particle is moving then the force on the particle is F × 10-9 N. The vector F is:

(A) -0.30 \hat{ i }+0.32 \hat{ j }-0.09 \hat{ k }

(B) -300 \hat{ i }+320 \hat{ j }-90 \hat{ k }

(D) -3.0 \hat{ i }+3.2 \hat{ j }-0.9 \hat{ k }

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

A charged particle carrying charge \(1\,\mu C\) is moving with velocity \((2 \hat{ i }+3 \hat{ j }+4 \hat{ k })\, ms ^{-1} .\) If an external magnetic field of \((5 \hat{ i }+3 \hat{ j }-6 \hat{ k }) \times 10^{-3}\, T\) exists in the region where the particle is moving then the force on the particle is \(\overline{ F } \times 10^{-9} N\). The vector \(\overrightarrow{ F }\) is :

Pick an option to check your answer.

Verified Solution

Correct Answer

(C) \(-30 \hat{ i }+32 \hat{ j }-9 \hat{ k }\)

Detailed explanation

\(\overrightarrow{ F }=q(\overrightarrow{ V } \times \overrightarrow{ B })\) (Force on charge particle moving in magnetic field)

\(\overrightarrow{ V } \times \overrightarrow{ B }=(2 \hat{ i }+3 \hat{ j }+4 \hat{ k }) \times(5 \hat{ i }+3 \hat{ j }-6 \hat{ k }) \times 10^{-3}\)

\(=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 2 & 3 & 4 \\ 5 & 3 & -6\end{array}\right| \times 10^{-3}\)

\(=[\hat{i}[-18-12]-\hat{j}[-12-20]+\hat{k}[6-15]] \times 10^{-3}\)

\(=[\hat{i}[-30]+\hat{j}[32]+\hat{k}[-9]] \times 10^{-3}\)

Force \(=10^{-6}[-30 \hat{i}+32 \hat{j}-9 \hat{k}] \times 10^{-3}\)

\(=10^{-9}[-30 \hat{ i }+32 \hat{ j }-9 \hat{ k }]\)

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