A: The magnetic field always accelerates a moving charge if the moving charge cuts the field lines.
R: When a moving charge cuts the magnetic field lines, the magnetic force on the charge is always non zero.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark 2.
C. If assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the assertion and reason question, we will analyze both statements step by step.

### Step 1: Understand the Assertion
The assertion states: "The magnetic field always accelerates a moving charge if the moving charge cuts the field lines."

- When a charged particle moves through a magnetic field, it experiences a magnetic force. This force is given by the equation:
\[ F = Q(\mathbf{v} \times \mathbf{B}) \]
where \( F \) is the magnetic force, \( Q \) is the charge, \( \mathbf{v} \) is the velocity vector of the charge, and \( \mathbf{B} \) is the magnetic field vector.

### Step 2: Analyze the Motion of the Charge
When the charge cuts through the magnetic field lines, it experiences a force that is perpendicular to both its velocity and the magnetic field. This results in circular motion.

- In circular motion, the direction of the velocity changes continuously, which means the charge is undergoing acceleration (even if the speed remains constant).

### Step 3: Understand the Reason
The reason states: "When a moving charge cuts the magnetic field lines, the magnetic force on the charge is always non-zero."

- The magnetic force will only be zero if the angle \( \theta \) between the velocity vector \( \mathbf{v} \) and the magnetic field vector \( \mathbf{B} \) is zero (i.e., they are parallel). However, when a charge is moving through a magnetic field and cutting the field lines, this angle is usually not zero, ensuring that the magnetic force is non-zero.

### Step 4: Conclusion
- Since the assertion is true (the magnetic field does accelerate a moving charge when it cuts the field lines) and the reason is also true (the magnetic force is non-zero when the charge cuts the field lines), we conclude that both statements are true, and the reason correctly explains the assertion.

### Final Answer
Both the assertion and reason are true, and the reason correctly explains the assertion. Therefore, the correct answer is option 1.

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