First slide

Magnetic force

Question

A charged particle has acceleration $\vec{a} = 2 \hat{i} + x \hat{j}$ in a magnetic field $\vec{B} = - 3 \hat{i} + 2 \hat{j} - 4 \hat{k}$ . Find the value if ‘x ’.

Moderate

A

$x = 2$
B

$x = 3$
C

$x = 4$
D

$x = - 3$

Solution

$W e k n o w t h a t, \vec{F} = q (\vec{v} \times \vec{B}) S o, M a g n e t i c f o r c e i s p e r p e n d i c u l a r t o f i e l d \bar{F} ⊥ \bar{B} ∴ \bar{a} ⊥ \bar{B} \Rightarrow \bar{a} . \bar{B} = 0 \Rightarrow (2 \hat{i} + x \hat{j}) . (- 3 \hat{i} + 2 \hat{j} - 4 \hat{k}) = 0 \Rightarrow - 6 + 2 x = 0 \Rightarrow x = 3$

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