Question

The dimensions of the quantity $E \times B$ where $E$ represents the electric field and $B$ the magnetic field may be given as

• A. $ MT^{-3} $
• B. $ M^{2}LT^{-5}A^{-2} $
• C. $ M^{2}LT^{-3}A^{-1} $
• D. $ MLT^{-2}A^{-2} $

Answer 1

Answer: (B)

$F=q v B$
$ B=\frac{F}{q v}=\frac{F}{I t v}$
$=\frac{\left[M L T^{-2}\right]}{[A T]\left[L T^{-1}\right]}=\left[M T^{-2} A^{-1}\right]$
$B=\frac{F}{q}=\left[M L T^{-3} A^{-1}\right]$
$E \times B=\left[M L T^{-3} A^{-1}\right] \times\left[M T^{-2} A^{-1}\right]$
$=\left[M^{2} L T^{-5} A^{-2}\right]$