Moving Charges and Magnetism Problem

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Homework Help Overview

The problem involves two charged particles, A and B, both with a charge of +6C, that are accelerated through the same potential difference before entering a magnetic field where they follow circular paths of different radii. The objective is to determine the ratio of their masses based on their motion in the magnetic field.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the final speed of the particles and the potential difference, questioning whether their velocities can be assumed equal. There is exploration of how to relate kinetic energy and electric energy in the context of the problem.

Discussion Status

Participants have provided insights into the relationship between potential difference and velocity, and how this affects the mass ratio of the particles. Some guidance has been offered regarding the use of energy equations and the implications of differing velocities on the circular paths of the particles.

Contextual Notes

The discussion includes considerations of the assumptions regarding equal charge and the implications of different masses and velocities on the circular motion of the particles in the magnetic field.

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Homework Statement



Two particles A and B having equal charges +6C, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular path of radii 2 and 3cm repectively. The ratio of mass of A and B is ______

Homework Equations



Force on the particle in a magnetic field = Bqv

In a circular path, mv^2/r = Bqv
→r = mv/Bq

The Attempt at a Solution



I don't know if I should consider their velocities to be equal.
If the velocities are equal, the r(A)/r(B) = 2/3 which is incorrect.
 
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Hello, anraphy. Welcome to PF!

Do you know how to relate the final speed of a particle to the potential difference through which it is accelerated?
 
Potential Difference and Velocity

TSny said:
Hello, anraphy. Welcome to PF!

Do you know how to relate the final speed of a particle to the potential difference through which it is accelerated?

E = Vq
→0.5mv^2=Vq
→v = √(2Vq/m)
OR
→V=0.5mv^2/q

where
V-potential difference
m-mass of the particle
v-velocity of the particle
E-energy of the particle
q-charge on the particle
 
OK. Good. Can you see how to use that?
 
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Hello, anraphy
The particles have different masses but have equal charge.So when it's accelerated through same potential difference, they will gain equal electric energy=Vq=kinetic energy
Vq=.5m1v12=.5m2v22
∴m1/m2=(v2/v1)2
Similarly when entering in Magnetic field due to different velocities they will follow different circular path of radii ra,rb respectively.
m1v1/ra=m2v2/rb=qB
 
Last edited:
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ImageUploadedByPhysics Forums1408248624.292973.jpg


I think I got it. Thank You :)
 

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