Question

A conducting wire in the shape of Y, with each side of length $l$ is moving in a uniform magnetic field B, with a uniform speed v as shown in the figure. The induced emf at the two ends X and Y of the wire will be

• A. zero
• B. 2Blv
• C. 2Blv sin($\theta$/2)
• D. 2Blv cos($\theta$/2)

Answer 1

The correct option is C 2Blv sin($\theta$/2)

From figure $b=lsin\left(\theta /2\right)$

Emf induced between X and Y

$E_{xy}=BvL$

where $L=2b$

$\therefore$ $E_{xy}=Bv\left(2b\right)=2Blvlsin\left(\theta /2\right)$