Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of $$\dfrac{1}{\sqrt{2}}$$ Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm/s, induced emf between points A and E is ________ mV.

$$\varepsilon = B \cdot v \cdot l_{\text{eff}}$$

Arm $$AB$$ is completely horizontal $$\implies$$ Vertical projection $$= 0$$

Arm $$DE$$ is completely horizontal $$\implies$$ Vertical projection $$= 0$$

Vertical projection of arm $$BC = 10 \cos 45^\circ = \frac{10}{\sqrt{2}} \text{ cm}$$

Vertical projection of arm $$CD = 10 \cos 45^\circ = \frac{10}{\sqrt{2}} \text{ cm}$$

$$l_{\text{eff}} = \frac{10}{\sqrt{2}} + \frac{10}{\sqrt{2}} = \frac{20}{\sqrt{2}} \text{ cm} = \frac{20}{\sqrt{2}} \times 10^{-2} \text{ m}$$

$$\varepsilon = \left(\frac{1}{\sqrt{2}}\right) \times (0.1) \times \left(\frac{20}{\sqrt{2}} \times 10^{-2}\right)$$

$$\varepsilon = 10^{-2} \times 10^3 \text{ mV} = 10 \text{ mV}$$