Moving electron under two magnetic fields

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SUMMARY

The discussion centers on calculating the Lorentz force acting on an electron under two magnetic fields, emphasizing the importance of incorporating the electron's mass into the calculations. Participants clarify that the exercise requires determining the force at a specific time, rather than calculating a trajectory, as no trajectory information is provided. The consensus is to use the known values of position, velocity, and magnetic field at time t to compute the force directly without introducing unnecessary variables.

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merdeka
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Homework Statement
A coil ##\vec{B}## a current of intensity ##i## created in ##M## a magnetic field ##\vec{B}_1##. A magnet ##A## created in ##M## a magnetic field ##\vec{B}_2## .

What is the force undergone by a charge particle ##q## with a velocity ##\vec{v}## that is in ##M## at time ##t## ?

Taking into account the mass of the electron.
Relevant Equations
##F=q\cdot v\cdot B\cdot\sin(\vec{v},\vec{B})##
Moving_particle_2_mag_fields_with_vectors_on_M.svg.png


In this question, I would have to calculate the force in respect to time. However, the question gives me the value of the mass of the electron. In my attempt, I didn't take that into account. I just replaced ##v## with ##\frac{d}{t}## and made the Lorentz force undergone by the particle inversely proportional, but this is probably not correct.
 
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Hi,

merdeka said:
the force in respect to time
I think the exercise asks for the force at time ##t## and doesn't want you to calculate a trajectory. (For which there is no information given anyway)
 
BvU said:
Hi,

I think the exercise asks for the force at time ##t## and doesn't want you to calculate a trajectory. (For which there is no information given anyway)
The question didn't give any information or value for a point in time.
 
So we agree on that. At time ##t##, position, velocity and field are known. There is no ##d## in the problem and you don't need it. Calculate in a straightforward manner with the equation you mention..
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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