Assertion: The energy of charged particle moving in uniform magnetic field does not change.
Reason: Work done by magnetic field on the charge is zero.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is the correct explanation of assertion.
C. If assertion is true but reason is false
D. If both assertion and reason are false.

Explanation

To analyze the given assertion and reason, we will follow these steps:

### Step 1: Understand the Assertion
The assertion states that "The energy of a charged particle moving in a uniform magnetic field does not change."

### Step 2: Understand the Reason
The reason provided is that "Work done by the magnetic field on the charge is zero."

### Step 3: Analyze the Force on a Charged Particle
When a charged particle moves in a magnetic field, it experiences a magnetic force given by the equation:
\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]
where:
- \( q \) is the charge,
- \( \mathbf{v} \) is the velocity vector of the charged particle,
- \( \mathbf{B} \) is the magnetic field vector.

### Step 4: Determine the Direction of the Force
The force \( \mathbf{F} \) is always perpendicular to both the velocity \( \mathbf{v} \) and the magnetic field \( \mathbf{B} \). This means that the magnetic force does not do any work on the charged particle.

### Step 5: Calculate Work Done
The work done \( W \) by a force is given by:
\[ W = \mathbf{F} \cdot \mathbf{dS} = F \cdot dS \cdot \cos(\theta) \]
Since the angle \( \theta \) between the force and the displacement is 90 degrees (as the force is perpendicular to the direction of motion), we have:
\[ W = F \cdot dS \cdot \cos(90^\circ) = 0 \]

### Step 6: Conclusion on Energy Change
Since no work is done on the charged particle, its kinetic energy remains constant. Thus, the assertion is true.

### Step 7: Evaluate the Reason
Since the reason correctly explains why the energy of the charged particle does not change, we conclude that both the assertion and the reason are true, and the reason is the correct explanation for the assertion.

### Final Answer
Both the assertion and reason are true, and the reason is the correct explanation of the assertion. Therefore, the correct option is:
**Option 1: Both assertion and reason are true, and reason is the correct explanation of assertion.**

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