Consider two thin identical conducting wires covered with very th… - Vidyadip

MCQ

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field $B_1,$ at its centre when a current $I$ passes through it.The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field $B_2$ at the centre of the loops when current $I/3$ passes through it. The ratio $B_1 : B_2$ is

A
$1:1$
✓
$1:3$
C
$1:9$
D
$9:1$

✓

Answer

Correct option: B.

$1:3$

b
For loop $\mathrm{B}=\frac{\mu_{0} \mathrm{nI}}{2 \mathrm{a}}$

where, $a$ is the radius of loop.

Then, $B_{1}=\frac{\mu_{0} I}{2 a}$

Now, for coil $\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{4 \pi} \cdot \frac{2 \mathrm{nA}}{\mathrm{x}^{3}}$

at the centre $x=$ radius of loop

$\mathrm{B}_{2} =\frac{\mu_{0}}{4 \pi} \cdot \frac{2 \times 3 \times(1 / 3) \times \pi(\mathrm{a} / 3)^{2}}{(\mathrm{a} / 3)^{3}} $

$=\frac{\mu_{0} \cdot 3 \mathrm{I}}{2 \mathrm{a}} $

$\therefore \frac{B_{1}}{B_{2}}=\frac{\mu_{0} I / 2 a}{\mu_{0} \cdot 3I / 2 a}$

$B_{1}: B_{2}=1: 3$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 4. Moving charges and magnetism→4. Moving charges and magnetism — all question types→Physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The minimum distance between an object and its real image formed by a convex lens is

If the luminous intensity of a 100 W unidirectional bulb is 100 candela, then total luminous flux emitted from the bulb is

Two magnets, each of magnetic moment $‘M’ $ are placed so as to form a cross at right angles to each other. The magnetic moment of the system will be

A man suffering from myopia can read a book placed at $10 cm$ distance. For reading the book at a distance of $60 cm$ with relaxed vision, focal length of the lens required will be......$cm$

The light when enters the human eye experiences most of the refraction while passing through

An electric line of force in the $xy$ plane is given by equation ${x^2} + {y^2} = 1$. A particle with unit positive charge, initially at rest at the point $x = 1,\;y = 0$ in the $xy$ plane

If an electron revolves in the path of a circle of radius of $0.5 \times 10^{-10} \mathrm{~m}$ at frequency of $5 \times 10^{15} \mathrm{cycles} / \mathrm{s}$ the electric current in the circle is (Charge of an electron $=1.6 \times 10^{-19} \mathrm{C}$ )

Current in the circuit is wattless, if.

A $20\,cm$ long metallic rod is rotated with $210\,rpm$ about an axis normal to the rod passing through its one end. The order end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field $0.2\,T$ parallel to the axis exists everywhere. The emf developed between the centre and the ring is $.......\,mV$.Take $\pi=\frac{22}{7}$

Two identical capacitors $A$ and $B$ are charged to the same potential $V$ and are connected in two circuits at $t = 0$ as shown in figure. The charges on the capahltors at a time $t = CR$ are, respectively: