Velocity of Rail on Metal Rails With Applied Magnetic Field My apologies for the

Question

Velocity of Rail on Metal Rails With Applied Magnetic Field

My apologies for the image being on its side.

Question)

A metal bar of mass M = 0.01kg and length L = 0.2m slides with negligible friction but with good electrical contact down between two vertical metal posts. The bar falls at a constant speed v (zero acceleration). The falling bar and the vertical metal posts have negligible electrical resistance, but the bottom rod is a resistor with resistance R = 2 ohms. Throughout the entire region there is a uniform magnetic field of magnitude B = 1.0 T coming straight out of the page. Find the value of v.

I don't really know where to start. I already know the answer from the answer key is 4.9 m/s. I need help getting to that answer. What rationale is required to solve this problem and what are some steps that can point me in the right direction?

Explanation / Answer

force on metal bar due to magnetic field and its velocity v = B^2l^2v/R

downward force is its weight=mg=0.01 x 9.8= 0.098 N

as rod is moving with a velocity,

B^2l^2v/R = mg

so, v = mgR/B^2l^2= 0.098 x 2 /(1^2 x 0.2^2)= 4.9 m/s

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