An electric charge + q +q moves with velocity v → = 3 i ^ + 4 j ^ + k ^ , in an electromagnetic field given by : E → = 3 i ^ + j ^ + 2 k ^ and B → = i ^ + j ^ + 3 k ^ . The y-component of the force experienced by + q is :

F → = q E → + v → × B → = q 3 i ^ + j ^ + k ^ + i ^ j ^ k ^ 3 4 1 1 1 + 3 = q 3 i ^ + j ^ + 2 k ^ + i ^ 1 2 - 1 - j ^ 9 - 1 + k ^ 3 - 4 = q 3 i ^ + j ^ + 2 k ^ + 12 i ^ - i ^ - 9 j ^ + j ^ + 3 k ^ - 4 k ^ q = 14 i ^ - 7 j ^ + k ^ = F y = - 7 q j ^

Physics - Magnetism Question with Solution | TestHub

PhysicsMagnetismMotion analysis in electric & magnetic fieldEasy2 minPYQ_2020

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An electric charge $+ q$ +q moves with velocity $\vec{v} = 3 \hat{i} + 4 \hat{j} + \hat{k},$ in an electromagnetic field given by : $\vec{E} = 3 \hat{i} + \hat{j} + 2 \hat{k}$ and $\vec{B} = \hat{i} + \hat{j} + 3 \hat{k}$ . The y-component of the force experienced by $+ q$ is :

Options:

Answer:

Solution:

$\vec{F} = q [\vec{E} + \vec{v} \times \vec{B}]$

$= q [3 \hat{i} + \hat{j} + \hat{k} + |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 4 & 1 \\ 1 & 1 & + 3 \end{matrix}|]$

$= q [3 \hat{i} + \hat{j} + 2 \hat{k} + \hat{i} (12 - 1) - \hat{j} (9 - 1) + \hat{k} (3 - 4)]$

$= q [3 \hat{i} + \hat{j} + 2 \hat{k} + 12 \hat{i} - \hat{i} - 9 \hat{j} + \hat{j} + 3 \hat{k} - 4 \hat{k}]$

$q = [14 \hat{i} - 7 \hat{j} + \hat{k}]$

$= F_{y} = - 7 q \hat{j}$

Stream:JEESubject:PhysicsTopic:MagnetismSubtopic:Motion analysis in electric & magnetic field

⏱ 2mℹ️ Source: PYQ_2020

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