GATE 2021 EE – Question 51
One coulomb of point charge moving with a uniform velocity $10\hat x$ m/s enters the region $x\ge0$ having a magnetic flux density $\vec B=(10y\hat x+10x\hat y+10\hat z)$ T. The magnitude of force on the charge at $x=0^+$ is ________ N.
($\hat x$, $\hat y$, and $\hat z$ are unit vectors along x-axis, y-axis, and z-axis, respectively.)
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Correct answer: 100
Explanation
The magnetic force is $\vec F=q\vec v\times\vec B=10\hat x\times(B_x,B_y,B_z)=10(0,-B_z,B_y)$. At $x=0$, $B_y=0$ and $B_z=10$, so $\vec F=-100\hat y$ N, of magnitude 100 N.