Magnetic flux- is this the correct way to solve it?

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The discussion centers on calculating the force required to pull a rectangular wire loop into a magnetic field at a constant velocity. The loop has specific dimensions, mass, and resistance, and the magnetic field strength is given. The calculations involve determining magnetic flux, induced voltage, and the resulting current through the loop. The final formula derived for the force incorporates the loop's dimensions, magnetic field strength, and velocity. The solution appears correct based on the applied equations and principles of electromagnetism.
t123123
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Homework Statement


As shown below, a rectangular wire loop of height 1.0 m, width 1.5 m, mass 0.10 kg, and resistance 10.0 Ω is pulled into a region of uniform magnetic field with magnitude 1.0 T pointing into the page (perpendicular to the plane of the loop). Determine the force necessary to pull the loop completely into the magnetic field region at a constant velocity of 5.0 m/s.

Homework Equations


magnetic flux=BA
inducedvoltage(V) =magnetic flux/dt
V=IR
F=qvB

The Attempt at a Solution


If magnetic flux is Z then
Z=BA
and V= Z/t = BA/ t
V=IR
IR=BA/t
Q/t *R =BA/t
then Q=BA/R
Q=1.0*(1.0*1.5)/10=.15C

F=.15C*5m/s*1.0T=0.75N
 
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t123123 said:
Determine the force necessary to pull the loop completely into the magnetic field region at a constant velocity of 5.0 m/s.
What is the emf induced in the loop when the wire is moving with a velocity of 5m/s? Use the motional emf equation.
What is the current through the loop?

Finally, what is the force acting on the wire due to this current?
 
Thank you! I think I figured it out.I needed to use F=ILB then F=V/RLB and F=dZ/dt/R*LB =BLv/R*LB which is L^2B^2V/R
 
t123123 said:
Thank you! I think I figured it out.I needed to use F=ILB then F=V/RLB and F=dZ/dt/R*LB =BLv/R*LB which is L^2B^2V/R
Looking good if you used L = side perpendicular to B and dZ/dt.
 
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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