Answer to Question #175126 in Electricity and Magnetism for Joshua Musyoki

Question

. A conductor of length 𝐿 moves at a steady speed vat right angles to a uniform magnetic field 

of flux density 𝐵. Show that the e.m.f. 𝐸 across the ends of the conductor is given by the 

equation 𝐸 = 𝐵𝑙𝑣.

Answer 1

Here l is the length of the conductor, B is the magnetic field, and v is the velocity.

The conductor is moving at 90⁰ to a magnetic field.

This conductor is covering a distance $\triangle s$ in time $\triangle t$ at 90⁰ to the magnetic field of the flux density, B.

Hence, $E=\frac{\triangle \phi }{\triangle t}$ , but we know that $\phi =BA$

$E=\frac{\triangle (BA) }{\triangle t}$

$E=Bl\frac{\triangle s}{\triangle t}$ , $\frac{\triangle s}{\triangle t}$ is the velocity

$E=Blv$