Question:
A charge \( q = 2\,\text{C} \) moves with velocity \( 3\,\text{m/s} \) perpendicular to a magnetic field \( B = 2\,\text{T} \). Force on charge is:
A charge \( q = 2\,\text{C} \) moves with velocity \( 3\,\text{m/s} \) perpendicular to a magnetic field \( B = 2\,\text{T} \). Force on charge is:
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When a charge moves perpendicular to a magnetic field ($\theta = 90^\circ$), the magnetic force is maximum ($F = qvB$).
If the charge moves parallel or antiparallel to the field ($\theta = 0^\circ$ or $180^\circ$), the force is zero ($F = 0$).
If the charge moves parallel or antiparallel to the field ($\theta = 0^\circ$ or $180^\circ$), the force is zero ($F = 0$).
Updated On: May 25, 2026
- $6\text{ N}$
- $12\text{ N}$
- $3\text{ N}$
- $0\text{ N}$
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Question:
The question asks to calculate the magnetic force acting on a moving charge when it enters a uniform magnetic field perpendicularly.
Step 2: Key Formula or Approach:
The magnetic force ($\vec{F}$) acting on a charge $q$ moving with a velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by the Lorentz force formula:
\[ F = q \cdot v \cdot B \cdot \sin\theta \] where $\theta$ is the angle between the velocity vector ($\vec{v}$) and the magnetic field vector ($\vec{B}$).
Step 3: Detailed Explanation:
• The magnetic force on a moving charge arises due to the interaction of the charge's own magnetic field (generated by its motion) with the external magnetic field.
• According to the problem statement, the charge is moving "perpendicular" to the magnetic field.
• This means the angle $\theta$ between the velocity vector $\vec{v}$ and the magnetic field vector $\vec{B}$ is $90^\circ$.
• We know that the value of $\sin(90^\circ) = 1$. This is the condition for maximum magnetic force.
• We are given the following values:
Charge, $q = 2\text{ C}$
Velocity, $v = 3\text{ m/s}$
Magnetic field, $B = 2\text{ T}$
• Substituting these values into the magnetic force formula:
\[ F = (2) \cdot (3) \cdot (2) \cdot \sin(90^\circ) \] \[ F = 2 \cdot 3 \cdot 2 \cdot 1 \] \[ F = 12\text{ N} \]
• Therefore, the magnitude of the force acting on the charge is $12\text{ N}$.
• The direction of this force is always perpendicular to both the velocity of the charge and the magnetic field, and can be determined using Fleming's Left-Hand Rule or the Right-Hand Rule.
Step 4: Final Answer:
The magnetic force acting on the given charge is $12\text{ N}$.
The question asks to calculate the magnetic force acting on a moving charge when it enters a uniform magnetic field perpendicularly.
Step 2: Key Formula or Approach:
The magnetic force ($\vec{F}$) acting on a charge $q$ moving with a velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by the Lorentz force formula:
\[ F = q \cdot v \cdot B \cdot \sin\theta \] where $\theta$ is the angle between the velocity vector ($\vec{v}$) and the magnetic field vector ($\vec{B}$).
Step 3: Detailed Explanation:
• The magnetic force on a moving charge arises due to the interaction of the charge's own magnetic field (generated by its motion) with the external magnetic field.
• According to the problem statement, the charge is moving "perpendicular" to the magnetic field.
• This means the angle $\theta$ between the velocity vector $\vec{v}$ and the magnetic field vector $\vec{B}$ is $90^\circ$.
• We know that the value of $\sin(90^\circ) = 1$. This is the condition for maximum magnetic force.
• We are given the following values:
Charge, $q = 2\text{ C}$
Velocity, $v = 3\text{ m/s}$
Magnetic field, $B = 2\text{ T}$
• Substituting these values into the magnetic force formula:
\[ F = (2) \cdot (3) \cdot (2) \cdot \sin(90^\circ) \] \[ F = 2 \cdot 3 \cdot 2 \cdot 1 \] \[ F = 12\text{ N} \]
• Therefore, the magnitude of the force acting on the charge is $12\text{ N}$.
• The direction of this force is always perpendicular to both the velocity of the charge and the magnetic field, and can be determined using Fleming's Left-Hand Rule or the Right-Hand Rule.
Step 4: Final Answer:
The magnetic force acting on the given charge is $12\text{ N}$.
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