Assertion: Magnetic field can not change the kinetic energy of moving charges.
Reason: Magnetic field can not change velocity vector.

Options

A. If both the assertion and reason are true and reason is a true explantion of the assertion.
B. If both the assertion and reason are true but the reason is not the correct explantion of the assertion.
C. If the assertion is true but reason false
D. If both the assertion and reason are false.

Answer

To analyze the given assertion and reason, let's break down the concepts step by step.

### Step 1: Understanding the Assertion
The assertion states that "Magnetic field cannot change the kinetic energy of moving charges."

**Explanation**: The kinetic energy (KE) of a charged particle is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the particle and \( v \) is its speed. The magnetic force acting on a charged particle is given by:
\[ F_m = q(\mathbf{v} \times \mathbf{B}) \]
where \( q \) is the charge, \( \mathbf{v} \) is the velocity vector, and \( \mathbf{B} \) is the magnetic field vector.

### Step 2: Work Done by Magnetic Force
The work done by a force is given by the dot product of the force and the displacement:
\[ W = \mathbf{F} \cdot \mathbf{d} \]
In the case of magnetic force, since the magnetic force is always perpendicular to the velocity vector of the charged particle, the work done by the magnetic force is:
\[ W = F_m \cdot d = |F_m| |d| \cos(90^\circ) = 0 \]
Thus, the work done by the magnetic force is zero.

### Step 3: Conclusion on Kinetic Energy
Since the work done by the magnetic force is zero, it implies that there is no change in the kinetic energy of the particle. Therefore, the assertion is true.

### Step 4: Understanding the Reason
The reason states that "Magnetic field cannot change the velocity vector."

**Explanation**: While the magnetic field does not change the magnitude of the velocity (speed), it does change the direction of the velocity vector. When a charged particle moves in a magnetic field, it experiences a magnetic force that causes it to move in a circular or helical path, altering the direction of its velocity vector continuously.

### Step 5: Conclusion on Reason
Therefore, the reason is false because the magnetic field does indeed change the direction of the velocity vector of a moving charge.

### Final Conclusion
- **Assertion**: True (Magnetic field cannot change the kinetic energy of moving charges).
- **Reason**: False (Magnetic field can change the direction of the velocity vector).

### Summary
- The assertion is true because the work done by the magnetic force is zero, leading to no change in kinetic energy.
- The reason is false because the magnetic field does change the direction of the velocity vector of charged particles.

---