Question

A metallic cube of side 15 cm moving along y-axis at a uniform velocity of 2ms⁻¹. In a region of uniform magnetic field of magnitude 0.5T directed along z-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be _______ mV.

Answer 1

150

Answer 2

Motional EMF is given by $\varepsilon = Blv$. The velocity $v$ is along the y-axis, and the magnetic field $B$ is along the z-axis. The induced electric field $E$ is in the direction of $v \times B$, which is along the -x axis. The potential difference is developed across the faces perpendicular to the x-axis. The length $l$ of the conductor in this direction is the side of the cube, $l = 15 \text{ cm} = 0.15 \text{ m}$. $\varepsilon = B \cdot l \cdot v$ $\varepsilon = (0.5 \text{ T}) \times (0.15 \text{ m}) \times (2 \text{ m/s})$ $\varepsilon = 0.15 \text{ V}$ Converting to millivolts: $\varepsilon = 0.15 \text{ V} \times 1000 \frac{\text{mV}}{\text{V}} = 150 \text{ mV}$