Embibe Experts Solutions for Chapter: Magnetic Effect of Current, Exercise 1: WBJEE 2018

A charged particle moves with constant velocity in a region, where no effect of gravity is felt but an electrostatic field $E$ together with a magnetic field $B$ may be present. Then, which of the following cases are possible?

A particle with charge $q$ moves with a velocity $v$ in a direction perpendicular to the directions of uniform electric and magnetic fields, $E$ and $B$ respectively, which are mutually perpendicular to each other. Which one of the following gives the condition for which the particle moves undeflected in its original trajectory?

A proton of mass $m$ moving with a speed $v$ $\left(<<c, \text{velocity of light in vacuum}\right)$ completes a circular orbit in time $T$ in a uniform magnetic field. If the speed of the proton is increased to $\sqrt{2}v$, what will be time needed to complete the circular orbit?

As shown in the figure, a wire is bent to form a $D$ -shaped closed loop, carrying current $I$, where the curved part is a semi-circle of radius $R$. The loop is placed in a uniform magnetic field $B$, which is directed into the plane of the paper. The magnetic force felt by the closed loop is

As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius $r$ concentrically inside a square of side $a,$ where $a:r=8:\pi$. A battery $B$ drives a current $I$ through the wire. If the battery $B$ and the gap $G$ are of negligible sizes, determine the strength of magnetic field at the common centre $O$.

A circular loop of radius $r$ of conducting wire connected with a voltage source of zero internal resistance produces a magnetic field $B$ at its centre. If instead, a circular loop of radius $2r$, made of same material, having the same cross-section is connected to the same voltage source, what will be the magnetic field at its centre?

A light charged particle is revolving in a circle of radius $r$ in electrostatic attraction of a static heavy particle with opposite charge. How does the magnetic field $B$ at the centre of the circle due to the moving charge depend on $r$ ?

A uniform current is flowing along the length of an infinite, straight, thin, hollow cylinder of radius $R$. The magnetic field $B$ produced at a perpendicular distance $d$ from the axis of the cylinder is plotted in a graph. Which of the following figures looks like the plot?