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 behavior of a charged particle moving in a magnetic field. Here’s a step-by-step breakdown:

### Step 1: Understand the scenario
A particle with mass \( m \) and charge \( q \) enters a transverse uniform magnetic field with induction \( B \). The particle has an initial kinetic energy \( T \).

### Step 2: Recall the properties of magnetic fields
When a charged particle moves through a magnetic field, it experiences a magnetic force that acts perpendicular to its velocity. This force causes the particle to undergo circular motion if the field is uniform and transverse to the velocity.

### Step 3: Analyze the effect of the magnetic field on kinetic energy
The key point to note is that the magnetic force does not do work on the charged particle. Since the force is always perpendicular to the direction of motion, it does not change the speed of the particle. Therefore, the kinetic energy of the particle remains constant.

### Step 4: Conclude the kinetic energy after 3 seconds
Since the kinetic energy does not change due to the magnetic field, the kinetic energy of the particle after 3 seconds will still be \( T \).

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

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