Please show all work and specify the correct answer at the bottom! A conducting

Question

Please show all work and specify the correct answer at the bottom!

A conducting bar slides without friction on two parallel horizontal rails that are 50 cm apart and connected by a wire at one end. The resistance of the bar and the rails is constant and equal to 0.10 . A uniform magnetic field is perpendicular to the plane of the rails. A 0.080-N force parallel to the rails is required to keep the bar moving at a constant speed of 0.50 m/s. What is the magnitude of the magnetic field?

Explanation / Answer

here,

Resistance, R = 0.10 ohms

Force, F = 0.080 N

Velocitry of rod, v = 0.50 m/s

Distance between the rails, d = 50 cm = 0.5 m

Magnatic force is given by expression,
F = I*B*d*Sin90
F = I*B*d

Also EMF = B*d*V = I*R
I = B*d*v/R

Therefore, magnatic force equation becomes
F = B^2*d^2*v/R

solving for magnatic field, B

B = sqrt(F*r/d^2*v)
B = sqrt(0.08*0.1/(0.5^2*0.5))

B = 0.253 T
or
B = 0.25 T ( two sig figures)

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