In the figure, a charged sphere of mass m and charge q starts sliding from rest on a vertical fixed circular track of radius R from the position shown. There exists a uniform and constant horizontal magnetic field of induction B . The maximum force exerted by the track on the sphere is -

Question

In the figure, a charged sphere of mass m and charge q starts sliding from rest on a vertical fixed circular track of radius R from the position shown. There exists a uniform and constant horizontal magnetic field of induction B . The maximum force exerted by the track on the sphere is - <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-5blqkksjoul3afxd.jpg" /> (A) mg (B) 3mg- qB√2 g R (C) 3mg+qB√2 g R (D) mg- qB√2 g R

Tardigrade Admin · Accepted Answer

Fm=q v B (directed radially outward) ∵ N- mg sin θ - q v B=(m v2/R) or N=(m v2/R)+mg sin θ +qvB θ =π / 2 Hence at θ =π / 2 Nm a x=(2 m g R/R)+mg+qB√2 g R =3mg+qB√2 g R Nm a x=3mg+qB√2 g R

Q. In the figure, a charged sphere of mass $m$ and charge $q$ starts sliding from rest on a vertical fixed circular track of radius $R$ from the position shown. There exists a uniform and constant horizontal magnetic field of induction $B$ . The maximum force exerted by the track on the sphere is -

$m g$

$3 m g - qB 2 g R$

$3 m g + qB 2 g R$

$m g - qB 2 g R$

$F_{m} = q v B$ (directed radially outward)
$∵ N - m g s in θ - q v B = \frac{m v ^{2}}{R}$
or $N = \frac{m v ^{2}}{R} + m g s in θ + q v B$
$θ = π /2$
Hence at $θ = π /2$
$N_{ma x} = \frac{2 m g R}{R} + m g + qB 2 g R$
$= 3 m g + qB 2 g R$
$N_{ma x} = 3 m g + qB 2 g R$

Q. In the figure, a charged sphere of mass m and charge q starts sliding from rest on a vertical fixed circular track of radius R from the position shown. There exists a uniform and constant horizontal magnetic field of induction B . The maximum force exerted by the track on the sphere is -

mg

3mg−qB2gR​

3mg+qB2gR​

mg−qB2gR​