Embibe Experts Solutions for Chapter: Magnetic Effect of Current and Magnetic Force on Charge or Current, Exercise 2: Exercise#2

A point charge $Q=\left(=3\times {10}^{-12} \mathrm{C}\right)$ rotates uniformly in a vertical circle of radius $R=1 \mathrm{mm}$. The axis of the circle is aligned along the magnetic axis of the earth. At what value of the angular speed $\omega$, the effective magnetic field at the center of the circle will be reduced to zero? (Horizontal component of earth's magnetic field is $30 \mathrm{\mu }\text{T}$)

A wire bent in the shape of a regular $n$ polygonal loop carries a steady current $I$. Let $l$ be the perpendicular distance of a given segment and $R$ be the distance of a vertex both from the centre of the loop. The magnitude of the magnetic field at the centre of the loop is given by,

Consider the regular array of vertical identical current carrying wires (with direction of current flow as indicated in the figure below) producing through a horizontal table. If we scatter some diamagnetic particles on the table, they are likely to accumulate,

Two infinitely long parallel wires carry currents of magnitude $I_1$ and $I_2$ and are at a distance $4 \mathrm{cm}$ apart. The magnitude of the net magnetic field is found to reach a non-zero minimum value between the two wires and $1 \mathrm{cm}$ away from the first wire. The ratio of the two currents and their mutual direction is,

Two infinitely long wires each carrying current $I$ along the same direction are made into the geometry as shown in the figure. The magnetic field at the point $P$ is, 

A rectangular region of dimensions $w\times I\left(w<<I\right)$ has a constant magnetic field into the plane of the paper as shown. On one side the region is bounded by a screen. On the other side positive ions of mass $m$ and charge $q$ are accelerated from rest and towards the screen by a parallel plate capacitor at constant potential difference $V<0$, and come out through a small hole in the upper plate. Which one of the following statements is correct regarding the charge on the ions that hit the screen? 

The current is flowing along the path $abcd$ of a cube (shown to the left) produces a magnetic field at the centre of cube of magnitude $B$. Dashed line depicts the non-conducting part of the cube. 

Consider a cubical shape shown to the right which is identical in size and shape to the left. If the same current now flows in along the path $daefgcd$, then the magnitude of magnetic field at the centre will be,

The magnetic field is uniform for $y>0$ and points into the plane. The magnetic field is uniform and points out of the plane for $y<0$. A proton denoted by filled circle leaves $y=0$ in the $y$-direction with some speed as shown below.

Which of the following best denotes the trajectory of the proton.