Question

A particle with charge 6 nC is moving in a uniform magnetic field $\overrightarrow{B}=\left(1.23T\right){\hat{a}}_z$ .The magnetic force on a particle is measured to be $\overrightarrow{F}=(4.5\times {10}^7){\hat{a}}_x+(7.5\times {10}^7){\hat{a}}_{y}N$
Select the correct statement(s).

• A. The dot product of velocity of particle and magnetic force is zero
• B. The component of velocity in y-direction is always zero
• C. (c)Magnetic field intensity in air is $9.78\times {10}^{5}A/m$
• D. Total force on particle when it is moving in both electric and magnetic field with electric field $\overrightarrow{E}=1{\hat{a}}_z$ volt / m is given as
  $(4.5\times {10}^7{\hat{a}}_x+7.5\times {10}^7{\hat{a}}_{y}N)$

Answer 1

Answer: (A), (C), (D)

Total force on particle when it is moving in both electric and magnetic field with electric field $\overrightarrow{E}=1{\hat{a}}_z$ volt / m is given as

$(4.5\times {10}^7{\hat{a}}_x+7.5\times {10}^7{\hat{a}}_{y}N)$
(a,c,d)
(a) Magnetic force and velocity are always normal to each other
thus dot product of them is zero
(b) $\overrightarrow{F}=q(\overrightarrow{V}\times \overrightarrow{B})$
$(4.5\times {10}^7{\hat{a}}_x+7.50\times {10}^7{a}_y)$ =
$(6\times {10}^{-9}\left[\right(x{\hat{a}}_x+y{\hat{a}}_y+z{\hat{a}}_z\left)\right]\times 1.23{\hat{a}}_z$
$\Rightarrow$
y-component of velocity is present so it is not zero
(c) $\overrightarrow{H}=\frac{B}{{\mu }_0}=\frac{1.23}{4\pi \times {10}^{-7}}$ = 9.78 $\times$ ${10}^5$ A/ m
(d) $\overrightarrow{E}=1{\hat{a}}_z$
$\overrightarrow{F}$ = Q$\overrightarrow{E}$ +q($\overrightarrow{V}$ $\times$ $\overrightarrow{B}$ )
$\overrightarrow{F}$ = ${\overrightarrow{F}}_E+{\overrightarrow{F}}_M$
${\overrightarrow{F}}_E$ = 6 $\times {10}^{-9}$ ${\hat{a}}_{z}N$
${\overrightarrow{F}}_M$ = $4.5\times {10}^7{\hat{a}}_x+7.5\times {10}^7{\hat{a}}_{y}N$
So,
$\overrightarrow{F}=4.5\times {10}^7{\hat{a}}_x+7.5\times {10}^7{\hat{a}}_y+6\times {10}^{-6}{\hat{a}}_{z}N$