First slide

Force on a charged particle moving in a magnetic field

Question

A proton of velocity $(3 \hat{i} + 2 \hat{j}) m s^{- 1}$ enters a field of magnetic induction $(2 \hat{j} + 3 \hat{k})$ tesla. The acceleration produced in the proton is (charge to mass ratio of proton = $0.96 \times 10^{8} C k g^{- 1}$ )

Easy

A

$2.8 \times 10^{8} (2 \hat{i} - 3 \hat{j})$
B

$2.88 \times 10^{8} (2 \hat{i} - 3 \hat{j} + 2 \hat{k})$
C

$2.8 \times 10^{8} (2 \hat{i} + 3 \hat{k})$
D

$2.88 \times 10^{8} (\hat{i} - 3 \hat{j} + 2 \hat{k})$

Solution

$\begin{array}{l} \vec{F} = q (\vec{V} \times \vec{B}) \\ a = \frac{F}{m} = \frac{q}{m} (V \times B) = |\begin{matrix} i & j & k \\ 3 & 2 & 0 \\ 0 & 2 & 3 \end{matrix}| \frac{q}{m} \end{array}$
$\begin{array}{l} = 0.96 \times 10^{8} [6 i - 9 j + 6 k] \\ = 2.88 \times 10^{8} [2 i - 3 j + 2 k] \end{array}$

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