Question

A charge q is moving with velocity v in a space where an electric field E and magnetic field B are present.the direction of velocity v is perpendicular to the direction of B .,the charge experiencesqE and magnetic force qvB.find out the dimensions of B E

Answer 1

Net force experienced by the charge :
F = qE + qVB

two physical quantities can be added when they have same dimensions.
dimension of qE and qVB must be equal to the dimension of the force.
$$\begin{gathered} F=\left[ML{T}^{-2}\right] \\ q=C=It=\left[AT\right] \\ \left[ML{T}^{-2}\right]=E\left[AT\right] \\ E\hspace{0.17em}=\left[ML{T}^{-3}{A}^{-1}\right] \\ magneticfield: \\ \left[ML{T}^{-2}\right]=\left[AT\right]\left[L{T}^{-1}\right]B \\ B=\left[M{T}^{-2}{A}^{-1}\right] \end{gathered}$$