Find Magnetic Force: Electron & Proton

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The discussion focuses on calculating the magnetic force on an electron and a proton moving through a uniform magnetic field. The user initially calculated the magnetic force for both particles, obtaining a force of 7.112e-14 for the electron and -7.112e-14 for the proton. However, the homework website flagged the proton's answer as incorrect due to not taking the absolute value of the force. The realization that the question asked for the magnitude of the force led to the correction of the error. This highlights the importance of carefully reading homework questions to avoid mistakes.
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Homework Statement


An electron that has a velocity with x component 2.1 × 106 m/s and y component 3.1 × 106 m/s moves through a uniform magnetic field with x component 0.035 T and y component -0.16 T. (a) Find the magnitude of the magnetic force on the electron. (b) Repeat your calculation for a proton having the same velocity.

Homework Equations


Fb=qVxB
q(VxBy-ByBx)

The Attempt at a Solution


I did the work, got an answer for part A which is 7.112e-14
Did the exact same procedure for part B and arrived at -7.112e-14, but the homework website is telling me it's wrong?! Not sure what my error is...
 
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The question asks for the magnitude of the force.
 
*facepalm*

Silly me, I should read questions more carefully. Forgot to absolute value on both parts, only with a it work out by luck! Thanks.
 
OK, good.
 

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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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