Question
A circular loop of radius r carries a current i. How should a long, straight wire carrying a current 4i be placed in the plane of the circle so that the magnetic field at the centre becomes zero?
✓
Answer
$\overrightarrow{\text{B}}$ due to loop $\frac{\mu_0\text{i}}{2\text{r}}$Let the straight current carrying wire be kept at a distance R from centre. Given I = 4i
$\overrightarrow{\text{B}}$ due to wire $\frac{\mu_0\text{i}}{2\pi\text{R}}=\frac{\mu_0\times4\text{i}}{2\pi\text{R}}$
Now, the $\overrightarrow{\text{B}}$ due to both will balance each other
Hence $\frac{\mu_0\text{i}}{2\text{r}}=\frac{\mu_04\text{i}}{2\pi\text{R}}\Rightarrow\text{R}=\frac{4\text{r}}{\pi}$
Hence the straight wire should be kept at a distance $\frac{4\pi}{\text{r}}$ from centre in such a way that the direction of current in it is opposite to that in the nearest part of circular wire. As a result the direction will $\overrightarrow{\text{B}}$ will be oppose.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A charged particle having a charge of $-2.0 \times 10^{-6} \mathrm{C}$ is placed close to a nonconducting plate having a surface charge density $4.0 \times 10^{-5} \mathrm{Cm}^{-2}$. Find the force of attraction between the particle and the plate.
→By using the method of dimension, check the accuracy of the following $\text{T}=\frac{\text{rh } \rho\text{g}}{2\cos\theta}$ where T is the surface tension, h is the height of the liquid in a capillary tube, $\rho$ is the density of the liquid, g is the acceleration due to gravity, $\theta$ is the angle of contact, and r is the radius of the capillary tube.
→The number of electrons in an insulator is of the same order as the number of electrons in a conductor. What is then the basic difference between a conductor and an insulator?
Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the dipole moment of the combination.
A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of $12m/s^2$. Find the displacement of the block during the first $0.2s$ after the start. Take $g = 10m/s^2$.
→Two strings of the same material and length under the same tension may vibrate with different fundamental frequency. Why?
A person aims a gun at a bird from a point at a horizontal distance of $100m$. If the gun can impart a speed of $500ms^{-1}$ to the bullet, at what height above the bird must he aim his gun in order to hit it?
→State the laws of limiting friction. Hence define coefficient of friction.
One kilogram molecule of a gas at $400 \ k$ expands isothermally until its volume is doubled. Find the amount of work done and heat produced.
→Describe Camot's cycle.