Two parallel metal rods form a plane inclined at 20.0° to the horizontal. The up

Question

Two parallel metal rods form a plane inclined at 20.0° to the horizontal. The upper end of the rods are connected together by a resistor of 128.0 . The lower end of the rods are held in an electrically insulating block. They are separated horizontally by a distance of 20.0 cm There is a uniform magnetic field of 0.100 T directed vertically upward. A metal bar of mass 0.10 g is sliding down the metal rods. What is the maximum speed of the bar? Assume: no frictional loss and that the rods are very long; g=9.8 m/s2.

Explanation / Answer

Maximum speed is when magnatic force is equal to gravitational force

Let i be the current in circuit and e is emf generated and v is max speed

=> i = e/R

flux = L*V*t ; where t is time

=> e = d(flux)/dt = LV

magnatic force = i*L*B = eLBcos(20)/R = B*V*l^2*cos(20)/R

gravitational force = mgsin(20)

both are equal

=> B*V*cos(20)*l^2/R = mgsin(20)

=> V = mgRtan(20)/Bl^2 = 0.1*9.8*128*0.364/(0.1*0.2*0.2) = 11415.04 m/s Answer

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