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SataSata
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Homework Statement
Magnetic Field B is going into the plane.
Bar is moving to the right with velocity v.
Neglect resistance of the conducting bar and all contacts.
a.) Determine the induced emf in the circuit.
b.) To maintain the uniform motion of the conductive bar, there must be an external force Fapp to pull the conductive bar. How much should Fapp be?
Homework Equations
Let the length of conducting bar in the triangle be ##l##
Hall Effect: ##emf = Blv ##
Faraday: ##emf = -d\Phi/dt##
##\Phi = BA##
##A=xl/2##
##l=xtan\theta##
##F_B=IlB##
The Attempt at a Solution
Using Faraday's Law:
##emf = -d\Phi/dt = -BdA/dt##
##dA/dt = dA/dx \times dx/dt##
##dA/dt = vxtan\theta##
##\therefore emf = -Bvxtan\theta##
Or, Using Hall Effect:
##emf = Blv = Bvxtan\theta##
Next, ##F_app = -F_B##
## Current I = emf/R = -Bvxtan\theta/R##
##F_app= IlB = B^2vx^2tan^2\theta/R##
Can anybody check if my attempt is correct? Are all the negative signs correct?
Faraday's Law and Hall Effect give different signs. Which one is correct?
Fapp sign is supposed to be positive or negative?