Assertion: Uniform electric and magnetic field are applied along Y-axis andZ-axis respectively. Kinetic energy of particle released at rest from origin depends only on the y-coordinate of particle.
Reason: Work done by the magnetic force is zero. Kinetic energy gained by the particle is only due to electric force

Options

A. If both assertion and reason are correct and reason is correct explanation of the assertion
B. If both assertion and reason are correct but reason is not correct explanation of the assertion
C. If assertion is correct but reason is incorrect.
D. If assertion is incorrect but reason is correct.

Answer

To solve the problem, we need to analyze the assertion and the reason provided in the question step by step.

### Step 1: Understanding the Assertion
The assertion states that when a particle is released from rest at the origin in a uniform electric field along the Y-axis and a uniform magnetic field along the Z-axis, the kinetic energy of the particle depends only on its Y-coordinate.

### Step 2: Analyzing the Forces
When the particle is released from rest, it experiences a force due to the electric field. The electric force \( F_E \) acting on a charged particle is given by:
\[ F_E = qE \]
where \( q \) is the charge of the particle and \( E \) is the electric field strength.

### Step 3: Magnetic Force Consideration
The magnetic force \( F_B \) acting on the particle is given by:
\[ F_B = q(\mathbf{v} \times \mathbf{B}) \]
where \( \mathbf{v} \) is the velocity of the particle and \( \mathbf{B} \) is the magnetic field. Since the particle starts from rest, its initial velocity \( \mathbf{v} = 0 \), which means that the magnetic force is also zero at the moment of release.

### Step 4: Work Done by the Forces
The work done by the magnetic force is zero because the magnetic force acts perpendicular to the direction of motion of the particle. The work done \( W \) by a force is given by:
\[ W = \mathbf{F} \cdot \mathbf{d} = F \cdot d \cdot \cos(\theta) \]
Since the magnetic force is perpendicular to the displacement of the particle, \( \theta = 90^\circ \) and thus \( \cos(90^\circ) = 0 \). Therefore, the work done by the magnetic field is zero.

### Step 5: Kinetic Energy Calculation
The kinetic energy \( K \) gained by the particle is solely due to the work done by the electric field. As the particle moves under the influence of the electric field, it gains kinetic energy given by:
\[ K = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the particle and \( v \) is its velocity, which is influenced only by the electric field.

### Step 6: Conclusion
From the analysis, we can conclude that:
- The assertion is correct: The kinetic energy of the particle does depend only on the Y-coordinate due to the electric field.
- The reason is also correct: The work done by the magnetic force is zero, and thus the kinetic energy gained by the particle is only due to the electric force.

Therefore, the correct answer is:
**A: Both assertion and reason are correct, and the reason is the correct explanation of the assertion.**