Q 12-06-079JEE MainJEE Main 2023 (11 Apr, Shift 2)Medium
A metallic cube of side $15\ \text{cm}$ moving along $y$-axis at a uniform velocity of $2\ \text{m s}^{-1}$. In a region of uniform magnetic field of magnitude $0.5\ \text{T}$ 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.
Numerical value type. Enter your answer.
Answer: 150
Charges in the cube feel $q\vec v\times\vec B\propto\hat j\times\hat k=\hat i$, so charge separates across the faces perpendicular to $x$ until the electric force balances it.
$$V=Bvl=0.5\times2\times0.15=0.15\ \text{V}=150\ \text{mV}$$
Solution by Sreeraj P, M.Sc Physics