Question

The mass of particle A is double the mass of particle B and the charge on both the particles is equal. If both the particles are moving perpendicular to the magnetic field B with equal speed, then the ratio of the magnetic force on particle A to particle B will be:
1. 1 : 1
2. 1 : 2
3. 2 : 1
4. 1 : 4

Answer 1

Correct Answer - Option 1 : 1 : 1

CONCEPT:

Lorentz force:

• It is defined as the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B. The entire electromagnetic force on the charged particle is called the Lorentz force and is given by,

​⇒ FL = qE + qvBsinθ 

• A charged particle experiences a force when it moves in a magnetic field.
• The magnetic force is given as,

​⇒ F = qvBsinθ

Where, F =  force due to magnetic field, m = mass, q = magnitude of charge, v = speed of charge, B = magnetic field and θ = angle between v and B

• When the velocity of a charged particle is perpendicular to a magnetic field, it describes a circular path.

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CALCULATION:

Given m_A = 2m_B, vA = vB = v, q_A = q_B = q, B_A = B_B = B and θ_A = θB = 90°

The magnetic force is given as (θ = 90°),

​⇒ F = qvBsinθ

​⇒ F = qvB.sin90

​⇒ F = qvB        -----(1)

• By equation 1 it is clear that the magnetic force on the charged particle when it is moving perpendicular to the magnetic field depends on the charge, speed, and magnetic field intensity but the magnetic force is independent of the mass of the particle.
• Since for particle A and particle B, the charge, speed, and magnetic field intensity are equal, so the magnetic force on both the particles will be equal.
• So the ratio of the magnetic force on particle A to particle B will be 1 : 1.
• Hence, option 1 is correct.