Magnetic Effects & Magnetism

JEE Main level, single correct, medium

219 of 276

Question 219 of 276

A charged particle carrying charge 1μC1\mu C is moving with velocity (2i^+3j^+4k^)ms−1(2\hat{i}+3\hat{j}+4\hat{k})m{s}^{-1}. If an external magnetic field of (5i^+3j^−6k^)×10−3T(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 F⃗×10−9N\vec{F}\times {10}^{-9}N . the vector F⃗\vec{F} is :

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Answer: (B) −30i^+32j^−9k^-30\hat{i}+32\hat{j}-9\hat{k}

Using the equation of force as,
F⃗=qV⃗×B⃗\vec{F}=q\vec{V}\times \vec{B}
F⃗=10−6×10−3∣i^j^k^23453−6∣\vec{F}={10}^{-6}\times {10}^{-3}\left|\begin{matrix}\hat{i} & \hat{j} & \hat{k} \\ 2 & 3 & 4 \\ 5 & 3 & -6\end{matrix}\right|
=(−30i^+32j^−9k^)×10−9N=\left(-30\hat{i}+32\hat{j}-9\hat{k}\right)\times {10}^{-9}N

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