Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Magnetic Effect of Electric Current, Exercise 3: Competitive Thinking

A rectangular loop of sides $10 \mathrm{cm}$ and $5 \mathrm{cm}$ carrying a current $I$ of $12 \mathrm{A}$ is placed in different orientations as shown in the figures below:

If there is a uniform magnetic field of $0.3 \mathrm{T}$ in the positive z direction, in which orientations the loop would be in $\left(\mathrm{i}\right)$ stable equilibrium and $\left(\mathrm{ii}\right)$ unstable equilibrium?

A conductor lies along the z-axis at $-1.5 \mathrm{m}\le z<1.5 \mathrm{m}$ and carries a fixed current of $10.0 \mathrm{A}$ in $-{\hat{\mathrm{a}}}_{\mathrm{z}}$ direction (see figure). For a field $\overrightarrow{B}=3.0\times {10}^{-4}{e}^{-0.2x}{\hat{\mathrm{a}}}_y \mathrm{T}$, find the power required to move the conductor at constant speed to $x=2.0 \mathrm{m}, \mathrm{y}=0 \mathrm{m}$ in $5\times {10}^{-3} \mathrm{s}$. Assume parallel motion along the x-axis

Two current-carrying coils have radii $r$ and $2r$ and have the same magnetic induction at their centres. The ratio of voltages applied across them is

A very long straight wire of radius $r$ carries current, $i$. The Intensity of the magnetic field, $B$ at a point, lying at a perpendicular distance $a\le r$ from the axis is directly proportional to

Magnetic induction produced at the centre of a circular loop carrying current is $B$. The magnetic moment of the loop of radius $R$ is $\left({\mu }_0=\right.$Permeability of free space$)$

The electron in the hydrogen atom circles around the proton with a speed of $2.2\times {10}^6 \mathrm{m} {\mathrm{s}}^{-1}$ in an orbit of radius $5\times {10}^{-11} \mathrm{m}$, what is the magnitude of the magnetic field produced at the proton?

If two streams of protons move parallel to each other in the same direction, then they

Two long current carrying thin wires, both with current $I$, are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle $\theta$ with the vertical. If wires have mass $\lambda$ per unit length then the value of $I$ is $(\mathrm{g}$ is gravitational acceleration)