Question

When a charged particle moving with velocity is subjected to a magnetic field of induction \(\rightarrow\) B , the force on it is non-zero. This implies that :

• A. Angle between \(\rightarrow\) B and \(\rightarrow\) V is necessarily 90°
• B. Angle between \(\rightarrow\) B and \(\rightarrow\) V can have any value other than 90°
• C. Angle between \(\rightarrow\) B and \(\rightarrow\) V can have any value other than Zero and 180°
• D. Angle between \(\rightarrow\) B and \(\rightarrow\) V is either Zero 180°

Answer 1

The Correct Option is C

To solve this question, we need to understand the concept of the force experienced by a charged particle moving in a magnetic field. The force on a charged particle moving with velocity \(\vec{V}\) in a magnetic field \(\vec{B}\) is given by the Lorentz force equation:

\(\vec{F} = q(\vec{V} \times \vec{B})\) 

Where:

• \(q\) is the charge of the particle.
• \(\vec{V}\) is the velocity vector of the particle.
• \(\vec{B}\) is the magnetic field vector.
• \(F = qVB\sin\theta\)

 

Where \(\theta\) is the angle between the vectors \(\vec{V}\) and \(\vec{B}\).

Analysis:

• The force will be non-zero when \(\sin\theta \neq 0\), implying that \(\theta\) cannot be 0° or 180°, as \(\sin 0 = \sin 180 = 0\). This means there is no component of velocity perpendicular to the magnetic field, hence no force.
• For any other angle, \(\theta\), between 0° and 180° excluding these two values, the force can be non-zero.
• The correct answer is: The angle between \(\vec{B}\) and \(\vec{V}\) can have any value other than Zero and 180°.