Answer
405.3k+ 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.
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.
![seo images](https://www.vedantu.com/question-sets/f9d09d04-eaee-4904-94e4-1e5a74b5ab43771164219797792265.png)
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
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)