Question

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R):

Assertion (A): An electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.
Reason (R): The magnetic field in that region is along the direction of velocity of the electron.

In the light of the above statements, choose the correct answer from the options given below:

• A. Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
• B. (A) is false but (R) is true
• C. Both (A) and (R) are true and (R) is the correct explanation of (A)
• D. (A) is true but (R) is false

Hint:

When a charged particle moves in a magnetic field, the force acting on the particle is always perpendicular to its velocity. This means the velocity does not change in magnitude, only direction. If the particle is moving in a straight line, the magnetic field cannot be parallel to the velocity.

Answer 1

The Correct Option is A

- Assertion (A) is true because an electron moving in a straight line with constant velocity in the presence of a magnetic field must not experience any force in the direction of motion. This implies the velocity of the electron is perpendicular to the magnetic field, so there is no magnetic force component along the velocity.

- Reason (R) is also true since the magnetic field must be perpendicular to the velocity for the force to not affect the motion of the electron. However, the statement that the magnetic field is "along the direction of velocity" contradicts the nature of the magnetic force, which acts perpendicular to both the magnetic field and the velocity. Thus, Reason (R) does not correctly explain Assertion (A).

Final Answer: Both (A) and (R) are true, but (R) is not the correct explanation of (A).

Answer 2

Step 1: Understand the Assertion (A) and Reason (R).
The assertion states: "An electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path."
The reason states: "The magnetic field in that region is along the direction of velocity of the electron."

Step 2: Analyze the assertion (A).
In the presence of a uniform magnetic field, the force on a moving charged particle (such as an electron) is given by the Lorentz force law: \[ \vec{F} = q(\vec{v} \times \vec{B}). \] Here, \( \vec{v} \) is the velocity of the electron, and \( \vec{B} \) is the magnetic field.
For the electron to move with constant velocity in a straight line, there must be no net force acting on it. This implies that the magnetic force must be zero. The magnetic force is zero only when the magnetic field is parallel to the velocity of the electron (i.e., \( \vec{v} \parallel \vec{B} \)), so the electron will not experience any perpendicular force, and thus it will continue moving in a straight line with constant velocity.

Step 3: Analyze the reason (R).
The reason states that the magnetic field is along the direction of the velocity of the electron. This is true because, when the magnetic field is parallel to the velocity of the electron, the magnetic force on the electron is zero, and thus the electron moves with constant velocity in a straight line.

Step 4: Conclusion.
While both (A) and (R) are true, the reason (R) does not explain the assertion (A) in the correct manner. The assertion explains that the electron is moving with constant velocity due to no magnetic force acting on it. However, the reason simply states that the magnetic field is along the velocity, which is true but does not explain why the electron moves in a straight line with constant velocity.

Final Answer:
Both (A) and (R) are true but (R) is NOT the correct explanation of (A).