Question

The force experienced by a charge $q$ moving with velocity $v$ in a magnetic field $B$ is maximum when the angle between $v$ and $B$ is

• A. $90^\circ$
• B. $0^\circ$
• C. $180^\circ$
• D. $45^\circ$

Hint:

Remember, the maximum force occurs at right angles between the velocity and the magnetic field.

Answer 1

The Correct Option is A

Step 1: Concept
The force experienced by a moving charge in a magnetic field is given by the Lorentz force law, which states that this force is proportional to the product of the charge, velocity, and magnetic field strength, as well as the sine of the angle between the velocity vector and the magnetic field vector.

Step 2: Meaning
The formula for the magnetic force on a moving charge $q$ with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is: \[\vec{F} = q (\vec{v} \times \vec{B})\] This can be simplified to express the magnitude of the force as: \[F = q v B \sin(\theta)\] where $F$ is the force, $q$ is the charge, $v$ is the velocity, $B$ is the magnetic field strength, and $\theta$ is the angle between the velocity vector and the magnetic field vector.

Step 3: Analysis
To find when this force is maximum, we need to maximize the expression $F = q v B \sin(\theta)$. Since $q$, $v$, and $B$ are all positive constants for a given scenario, maximizing $F$ reduces to finding the value of $\theta$ that maximizes $\sin(\theta)$. The sine function reaches its maximum value of 1 when $\theta = 90^\circ$. Therefore, the force is maximum when the angle between the velocity vector and the magnetic field vector is $90^\circ$.

Step 4: Conclusion
This conclusion aligns with the principle that the force on a moving charge in a magnetic field is maximized when the charge's motion is perpendicular to the magnetic field lines. Final Answer: (A)