Question

A charged particle of mass $$m$$ and charge $$q$$ travels on a circular path of radius $$r$$ that is perpendicular to a magnetic field $$B.$$ The time taken by the particle to complete one revolution is

A. $$\frac{{2\pi {q^2}B}}{m}$$
B. $$\frac{{2\pi mq}}{B}$$
C. $$\frac{{2\pi m}}{{qB}}$$  
D. $$\frac{{2\pi qB}}{m}$$
Answer :   $$\frac{{2\pi m}}{{qB}}$$
Solution :
Equating magnetic force to centripetal force,
$$\frac{{m{v^2}}}{r} = qvB\sin {90^ \circ }$$
Time to complete one revolution,
$$T = \frac{{2\pi r}}{v} = \frac{{2\pi m}}{{qB}}$$

Releted MCQ Question on
Electrostatics and Magnetism >> Magnetic Effect of Current

Releted Question 1

A conducting circular loop of radius $$r$$ carries a constant current $$i.$$ It is placed in a uniform magnetic field $${{\vec B}_0}$$ such that $${{\vec B}_0}$$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is

A. $$ir\,{B_0}$$
B. $$2\pi \,ir\,{B_0}$$
C. zero
D. $$\pi \,ir\,{B_0}$$
View Answer
Releted Question 2

A battery is connected between two points $$A$$ and $$B$$ on the circumference of a uniform conducting ring of radius $$r$$ and resistance $$R.$$ One of the arcs $$AB$$  of the ring subtends an angle $$\theta $$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

A. proportional to $$2\left( {{{180}^ \circ } - \theta } \right)$$
B. inversely proportional to $$r$$
C. zero, only if $$\theta = {180^ \circ }$$
D. zero for all values of $$\theta $$
View Answer
Releted Question 3

A proton, a deuteron and an $$\alpha - $$ particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $${r_p},{r_d},$$  and $${r_\alpha }$$ denote respectively the radii of the trajectories of these particles, then

A. $${r_\alpha } = {r_p} < {r_d}$$
B. $${r_\alpha } > {r_d} > {r_p}$$
C. $${r_\alpha } = {r_d} > {r_p}$$
D. $${r_p} = {r_d} = {r_\alpha }$$
View Answer
Releted Question 4

A circular loop of radius $$R,$$ carrying current $$I,$$ lies in $$x - y$$  plane with its centre at origin. The total magnetic flux through $$x - y$$  plane is

A. directly proportional to $$I$$
B. directly proportional to $$R$$
C. inversely proportional to $$R$$
D. zero
View Answer

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Magnetic Effect of Current

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Heat and ThermodynamicsThermodynamicsThermal ExpansionConductionRadiationCalorimetryKinetic Theory of Gases
Electrostatics and MagnetismElectric ChargesElectric FieldElectric PotentialCapacitors and DielectricsMagnetic Effect of CurrentMagnetic MaterialsElectromagnetic WavesElectric CurrentElectromagnetic InductionAlternating CurrentSemiconductors and Electronic Devices
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