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Analysis of Force Equation

Question

When a charged particle moving with velocity $\to V$ is subjected to a magnetic field of induction $\to B$ , the force on it is non-zero. This implies the
Angle between $\to V$ and $\to B$ is necessary $90^{o}$
Angle between $\to V$ and $\to B$ can have a value other than $90^{o}$
Angle between $\to V$ and $\to B$ can have a value other than zero and $180^{o}$
Angle between $\to V$ and $\to B$ is either zero or $180^{o}$

A

Angle between

\to V

and

\to B

is either zero or

180^{o}

B

Angle between

\to V

and

\to B

is necessary

90^{o}

C

Angle between

\to V

and

\to B

can have a value other than

90^{o}

D

Angle between

\to V

and

\to B

can have a value other than zero and

180^{o}

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Solution

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Force on a charged particle moving in a magnetic field is

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

Let the angle between $\to v$ and $\to B$ be $θ$

Hence $∣ ∣ \to F ∣ ∣ = q v B s i n θ \neq 0$

$⟹ s i n θ \neq 0$

$⟹ θ \neq 0^{\circ}, 180^{\circ}$

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