A particle of mass m, charge q and kinetic energy T enters in a transverse uniform magnetic field of induction B. After the 3 s, the kinetic energy of the particle will be

Options

A. 3T
B. 2T
C. T
D. 4T

Answer

To solve the problem, we need to understand the effect of a magnetic field on a charged particle. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the scenario
A particle with mass \( m \), charge \( q \), and initial kinetic energy \( T \) enters a uniform magnetic field with induction \( B \). The magnetic field is transverse, meaning it is perpendicular to the direction of the particle's motion.

**Hint:** Remember that the magnetic field affects the motion of charged particles but does not change their kinetic energy.

### Step 2: Analyze the effect of the magnetic field
When a charged particle moves through a magnetic field, it experiences a magnetic force that is perpendicular to both the velocity of the particle and the magnetic field. This force causes the particle to move in a circular path, but it does not do work on the particle.

**Hint:** Recall that the work done by a force is related to the change in kinetic energy. If the force is perpendicular to the velocity, no work is done.

### Step 3: Conclude about the kinetic energy
Since the magnetic force does not do any work on the particle, the kinetic energy of the particle remains unchanged as it moves through the magnetic field. Therefore, after 3 seconds, the kinetic energy of the particle will still be \( T \).

**Hint:** Think about the conservation of energy in the context of forces acting on the particle.

### Final Answer
The kinetic energy of the particle after 3 seconds in the magnetic field will be \( T \).