A tightly wound long solenoid has 'n' turns per unit length, a radius ' r ' and carries a current I. A particle having charge ' q ' and mass 'm' is projected from a point on the axis in a direction perpendicular to the axis. The maximum speed of the particle for which the particle does not strike the solenoid is

Question

A tightly wound long solenoid has 'n' turns per unit length, a radius ' r ' and carries a current I. A particle having charge ' q ' and mass 'm' is projected from a point on the axis in a direction perpendicular to the axis. The maximum speed of the particle for which the particle does not strike the solenoid is (A) (μ0 nIqr / m ) (B) (μ0 nIqr /2 m ) (C) (μ0 nIqr /4 m ) (D) (μ0 nIqr /8 m )

Tardigrade Admin · Accepted Answer

F B = qvB sin θ θ = 90° F B = qvB F C =( mv 2/ r ) F B = F C qvB =( mv 2/(( r )2)) v =( qrB /2 m ) B =μ0 nI v =( qr μ0 nI /2 m )

$\frac{μ _{0} n I q r}{m}$

$\frac{μ _{0} n I q r}{2 m}$

$\frac{μ _{0} n I q r}{4 m}$

$\frac{μ _{0} n I q r}{8 m}$

$F_{B} = q v B sin θ θ = 9 0^{\circ}$
$F_{B} = q v B$
$F_{C} = \frac{m v ^{2}}{r}$
$F_{B} = F_{C}$
$q v B = \frac{m v ^{2}}{( \frac{r}{2} )}$
$v = \frac{q r B}{2 m}$
$B = μ_{0} n I$
$v = \frac{q r μ _{0} n I}{2 m}$

mμ0​nIqr​

2mμ0​nIqr​

4mμ0​nIqr​

8mμ0​nIqr​

FB​=qvBsinθθ=90∘ FB​=qvB FC​=rmv2​ FB​=FC​ qvB=(2r​)mv2​ v=2mqrB​ B=μ0​nI v=2mqrμ0​nI​

$\frac{μ _{0} n I q r}{m}$

$\frac{μ _{0} n I q r}{2 m}$

$\frac{μ _{0} n I q r}{4 m}$

$\frac{μ _{0} n I q r}{8 m}$

$F_{B} = q v B sin θ θ = 9 0^{\circ}$
$F_{B} = q v B$
$F_{C} = \frac{m v ^{2}}{r}$
$F_{B} = F_{C}$
$q v B = \frac{m v ^{2}}{( \frac{r}{2} )}$
$v = \frac{q r B}{2 m}$
$B = μ_{0} n I$
$v = \frac{q r μ _{0} n I}{2 m}$