BITSAT 2011 Paper

The metal rod of length 1m is rotated about one of its ends in a plane at right angle to a uniform
magnetic field of induction 2.5×10−3Wb⋅m−2 .
The rod is rotating with the angular speed of 1800 rpm.
Calculate the emf induced between the ends of the metal rod.
Convert the unit of the angular speed in the SI system of units.
ω=(1800rpm)(‌

2π

60

)rad⋅s−1
⇒ω=(1800rpm)(‌

2×3.14

60

)rad⋅s−1
⇒ω=188.4rad⋅s−1
Hence, the angular speed of the rotating end of the rod is 188.4rad⋅s−1 .
Rewrite the equation (2) for the linear speed v of the one end of the rod moving around its other end.
v=‌

L

2

ω
Here, L is the length of the rod which is the diameter for the circular path for the rotating end of the rod
and ω is the angular speed of the rod end.
Substitute ‌

L

2

ω for v in equation (1). e=BL(‌

L

2

ω)
⇒e=‌

BL2ω

2

Substitute 2.5×10−3Wb⋅m−2 for B,1m for L and 188.4rad⋅s−1 for ω in the above equation.

⇒e=235.5×10−3V
⇒e=0.235V
⇒e≈0.24V