An electric charge -q moves with velocity v-3-4-k- in the presence of electric and magnetic fields given by E-3-2k- and B-3k- The y-component of the force experienced by -q is -

Using Lorentz's force equation, F=q(E+(v×B)) Given, E=3î+ĵ+2k̂ V=3î+4ĵ+k̂ nbsp; B=î+ĵ 3k̂ Putting values in nbsp;F we get, F=q[3î+ĵ+2k̂+(3î+4ĵ+k̂)× ( ...

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Standard XII

Physics

Motional EMF in an Open Conductor

An electric c...

Question

An electric charge $+ q$ moves with velocity $\to v = 3^i + 4^j +^k$ in the presence of electric and magnetic fields given by $\to E = 3^i +^j + 2^k$ and $\to B =^i +^j - 3^k$ . The y-component of the force experienced by $+ q$ is ?

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Solution

Using Lorentz's force equation,

$\to F = q (\to E + (\to v \times \to B))$

Given,

$\to E = 3^i +^j + 2^k \to V = 3^i + 4^j +^k \to B =^i +^j - 3^k$

Putting values in $\to F$ we get,

$\to F = q [3^i +^j + 2^k + (3^i + 4^j +^k) \times (^i +^j - 3^k)]$

$= q [3^i +^j + 2^k + 3^k + 9^j - 4^k - 12^i +^j -^i]$

$\to F = q [- 10^i + 11^j +^k]$

$| {\to F}_{y} | = 11 q$

 Hence, option (b) is the correct answer.

Why this question ?

To familiarize oneself how to use Lorentz force equation in different scenarios and to make vector calcualtion familiar.

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Motional EMF in an Open Conductor

Standard XII Physics

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An electric charge +q moves with velocity →v=3^i+4^j+^k in the presence of electric and magnetic fields given by →E=3^i+^j+2^k and →B=^i+^j−3^k. The y-component of the force experienced by +q is ?

An electric charge $+ q$ moves with velocity $\to v = 3^i + 4^j +^k$ in the presence of electric and magnetic fields given by $\to E = 3^i +^j + 2^k$ and $\to B =^i +^j - 3^k$ . The y-component of the force experienced by $+ q$ is ?