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

Question

The dimensions of the quantity E × B where E represents the electric field and B the magnetic field may be given as (A)  MT-3  (B)  M2LT-5A-2  (C)  M2LT-3A-1  (D)  MLT-2A-2

Tardigrade Admin · Accepted Answer

F=q v B B=(F/q v)=(F/I t v) =([M L T-2]/[A T][L T-1])=[M T-2 A-1] B=(F/q)=[M L T-3 A-1] E × B=[M L T-3 A-1] ×[M T-2 A-1] =[M2 L T-5 A-2]

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

$M T^{- 3}$

$M^{2} L T^{- 5} A^{- 2}$

$M^{2} L T^{- 3} A^{- 1}$

$M L T^{- 2} A^{- 2}$

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

Q. The dimensions of the quantity E×B where E represents the electric field and B the magnetic field may be given as

MT−3

M2LT−5A−2

M2LT−3A−1

MLT−2A−2