A particle of mass $$M$$ and charge $$Q$$ moving with velocity $$\vec v$$ describe a circular path of radius $$R$$ when subjected to a uniform transverse magnetic field of induction $$B.$$ The work done by the field when the particle completes one full circle is
A.
$$\left( {\frac{{M{v^2}}}{R}} \right)2\pi R$$
B.
zero
C.
$$BQ2\pi R$$
D.
$$BQv2\pi R$$
Answer :
zero
Solution :
The workdone, $$dW = Fds\cos \theta $$
The angle between force and displacement is 90°.
Therefore work done is zero.
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 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 $$2\left( {{{180}^ \circ } - \theta } \right)$$
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 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