The magnetic force acting on a charged partic | vedclass

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Question

(A) The magnetic force $\vec{F}$ on a charged particle is given by the Lorentz force formula: $\vec{F} = q(\vec{v} 	imes \vec{B})$.Given:$q = 2\,\mu

Vedclass · Accepted Answer

$8\, N$ in $z-$ direction

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(A) The magnetic force $\vec{F}$ on a charged particle is given by the Lorentz force formula: $\vec{F} = q(\vec{v} 	imes \vec{B})$.Given:$q = 2\,\mu C = 2 	imes 10^{-6}\, C$$\vec{v} = (2\hat{i} + 3\hat{j}) 	imes 10^6\, m/s$$\vec{B} = 2\hat{j}\, T$Substituting the values:$\vec{F} = (2 	imes 10^{-6}) 	imes [(2\hat{i} + 3\hat{j}) 	imes 10^6] 	imes (2\hat{j})$$\vec{F} = 2 	imes [ (2\hat{i} 	imes 2\hat{j}) + (3\hat{j} 	imes 2\hat{j}) ]$Since $\hat{i} 	imes \hat{j} = \hat{k}$ and $\hat{j} 	imes \hat{j} = 0$:$\vec{F} = 2 	imes [ 4\hat{k} + 0 ] = 8\hat{k}\, N$.Thus,the force is $8\, N$ in the $z-$ direction.

The magnetic force acting on a charged particle of charge $2\,\mu C$ in a magnetic field of $2\, T$ acting in the $y-$ direction,when the particle velocity is $(2\hat{i} + 3\hat{j}) \times 10^6\, m/s$ is:

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