As shown in the figure a metal rod makes contact and complete the circuit. The circuite is perpendicular to the magnetic field with `B=0.15`tesla. If the resistance is `3Omega` force needed to move the rod as indicated with a constant speed of `2m//sec` is

Options

A. `3.75xx10^(-3)N`
B. `2.75xx10^(-3)N`
C. `6.57xx10^(-4)N`
D. `4.36xx10^(-4)N`

Answer

A

Explanation

The emf induced in the rod causes a currect to flow anticlockwise direrction in the circuit. Because of this currect in the rod, it experiences a force to the left due to the magnetic field. In order to pull the rod to the right with constant speed, this force must be balanced by the puller.
The emf in the rod is
`|epsi|=Blv=(0.15 T)(0.5m)(2 m s^(-1))=0.15V`
Current induced in the rod is `I=(|epsi|)/(R)=(015V)/(3Omega)=0.05A`
`:. F=Il B sin90
^(@)=(0.05A)(0.05m)(0.015T)(1)`
`=3.75xx10^(-3)N`