First slide

Magnetic force

Question

A proton beam moves through a region of space where there exists a uniform magnitude 4.0 T along z-axis. The protons have a velocity of $4 \times 10^{5} m / s$ in the x-z plane at an angle $30^{0}$ to the positive z-axis. Then the force acting on the proton is $- x \times 10^{- 14} \hat{j} N$ , find $x = ?$

Moderate

Solution

$∴ \vec{F} = q (\vec{v} \times \vec{B}) = 1.6 \times 10^{- 19} (4 \times 10^{5}) \times [(\sin 30^{o} \hat{i} + \cos 30^{o} \hat{k}) \times 4 \hat{k}] \Rightarrow \vec{F} = - 12.8 \times 10^{- 14} \hat{j} ∴ x = 12.8$

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