The Question is from neet-physics electrostatic-charges-and-fields , and it was created by the author SUBHANI

Question

Two identical charged particles are projected into a uniform electric field. Particle A is projected with velocity $v$ perpendicular to the field, while particle B is projected with velocity $2v$ at an angle of $30^\circ$ to the field. Which particle experiences a larger force due to the electric field?

SUBHANI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
 **Primary Concept**: Force on a charged particle in an electric field
 **Related Topics**: Electric field, vectors, projectile motion
 **Prerequisites**: Understanding of electric force, vector components
## SOLUTION PATHWAY
**Given Information**:
  * Two identical charged particles (same charge $q$ and mass $m$)
  * Particle A: velocity $v_A = v$, angle with field $	heta_A = 90^\circ$
  * Particle B: velocity $v_B = 2v$, angle with field $	heta_B = 30^\circ$
  * Uniform electric field $\vec{E}$
**Method & Steps**:
 1. Determine the force on each particle due to the electric field.
  Reasoning: The force on a charged particle in an electric field is given by $\vec{F} = q\vec{E}$. The velocity of the particle does not affect the force.
  Formula/Rule: $\vec{F} = q\vec{E}$
 2. Analyze the forces.
  Working: Since the particles are identical and the electric field is uniform, the magnitude of the force on each particle is the same: $F = qE$. The direction of the force is the same for both particles (along the direction of the electric field).
  Key Point: The force due to the electric field is independent of the particle's velocity.
 3. Compare the forces.
  Result: Both particles experience the same force.
  Verification: The force is solely determined by the charge and the electric field strength, which are identical for both particles.
 ## OPTION ANALYSIS
A :x: The velocity of the particle doesn't affect the force due to the electric field.
B :x: The velocity of the particle doesn't affect the force due to the electric field.
C ✓: Both particles experience the same force because the force is given by $F = qE$, where $q$ is the charge and $E$ is the electric field strength. Since both particles have the same charge and are in the same electric field, the force on them is the same.
D :x: The force can be determined from the given information.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Assuming that the force depends on the velocity: The force on a charged particle in a uniform electric field is independent of its velocity.
  2.Ignoring the vector nature of the force and velocity: While the velocity affects the trajectory of the particle, it does not affect the magnitude of the force due to the electric field.
 **Quick Tips**:
  1.Remember the fundamental formula: $F = qE$
  2.Focus on the given information: The problem states that the particles are identical and in a uniform electric field.

SUBHANI · Answer

Particle A

SUBHANI · Answer

Particle B

SUBHANI · Answer

The correct Option is "Both experience the same force"

SUBHANI · Answer

Cannot be determined

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