Answer

Verified

393.9k+ views

**Hint:**Biot-Savart law gives the magnetic field produced due to a current carrying conductor. To find the intensity of the magnetic field at the centre of the current carrying rod of length $l$, which is carrying a current $I$, we can use this law.

**Formula Used:**$dB= \dfrac{\mu_{0}}{4\pi}\times \dfrac{I dl Sin\theta}{r^{2}}$

**Complete step-by-step solution**

Biot-Savart law states that the magnetic field $B$ produced at any point near a current-carrying conductor is proportional to the material of the medium $\mu_{0}$, the current $I$ flowing in the conductor, the small length of the wire $d\;l$ involved, and inversely proportional to distance $r$ between the point and the conductor.

Mathematically, $dB \propto \mu_{0}$, $dB\propto I$, $dB \propto dl$ and $dB \propto \dfrac{1}{r^{2}}$

Then, $dB= \dfrac{\mu_{0}}{4\pi}\times \dfrac{I dl Sin\theta}{r^{2}}$, where $\theta$ is the angle between $d\;l$ and $r$.

The Biot-Savart law is given on the basis of magnetostatics and it gives the relationship between the current and the magnetic field for any shape of conductor. It is derived from the ampere's circuital law.

Here, given that A and B are at distances X and 3X from its center on opposite sides.

From $dB \propto \dfrac{1}{r^{2}}$, but since the points A and B lie on the axial line of the given rod, we get, $dB\propto\dfrac{1}{r^{3}}$, then on substitution we get,

$\dfrac{B_{A}}{B_{B}}=\dfrac{(3X)^{3}}{X^{3}}$

$\implies \dfrac{B_{A}}{B_{B}}=\dfrac{27}{1}$

**$\therefore C.27:1$ is the required correct answer.**

**Note:**From the formula, it is clear that the magnetic field produced depends on the nature of the conductor and the amount of current flowing in the circuit. Note that, we are taking the cross product of the current and the small length, which is why we have a $\theta$ in the equation. Also, note that the length of the rod is not taken into account for calculation.

Recently Updated Pages

Which of the following materials is likely to have class 8 physics CBSE

What is a quasar What is their importance class 8 physics CBSE

Identify the parts which vibrate to produce sound in class 8 physics CBSE

Write the relation between liter and cm3 class 8 physics CBSE

Define the terms a ray of light and a beam of ligh class 8 physics CBSE

Suppose you are in a car and it is raining heavily class 8 physics CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail

Name 10 Living and Non living things class 9 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths