A long curved conductor carries a current $I$ (I is a vector). A small current element of length $d l$, on the wire induces a magnetic field at a point, away from the current element. If the position vector between the current element and the point is $r$, making an angle with current element then, the induced magnetic field density; $d B$ (vector) at the point is $\left(\mu_{0}=\right.$ permeability of free space $)$
- $\frac{\mu_{0} \text { Id } l \times r }{4 \pi r}$ (perpendicular to the current element $d l$ )
- $\frac{\mu_{0} I \times r \times d l}{4 \pi r^{2}}$ (perpendicular to the current element $d l$ )
- $\frac{\mu_{0} I \times d l}{r}$ (perpendicular to the plane containing the current element and position vector $r$ )
- $\frac{\mu_{0} I \times d l}{4 \pi r^{2}}$ (perpendicular to the plane containing current element and position vector $r$ )
The Correct Option is B
Solution and Explanation
$d B=\frac{\mu_{0} I \times r \times d l}{4 \pi r^{2}}$
Top Questions on Magnetic Field Due To A Current Element, Biot-Savart Law
- Two parallel long current carrying wire separated by a distance $2r$ are shown in the figure. The ratio of magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is ___.
- JEE Main - 2024
- Physics
- Magnetic Field Due To A Current Element, Biot-Savart Law
- Three vectors \(\overrightarrow{OP}\), \(\overrightarrow{OQ}\), and \(\overrightarrow{OR}\) each of magnitude \(A\) are acting as shown in figure. The resultant of the three vectors is \(A \sqrt{x}\). The value of \(x\) is ______.
- JEE Main - 2024
- Physics
- Magnetic Field Due To A Current Element, Biot-Savart Law
- The angle between vector \( \vec{Q} \) and the resultant of \( (2\vec{Q} + 2\vec{P}) \) and \( (2\vec{Q} - 2\vec{P}) \) is:
- JEE Main - 2024
- Physics
- Magnetic Field Due To A Current Element, Biot-Savart Law
- Two circular coils \(P\) and \(Q\) of \(100\) turns each have the same radius of \(\pi \, \text{cm}\). The currents in \(P\) and \(Q\) are \(1 \, \text{A}\) and \(2 \, \text{A}\) respectively. \(P\) and \(Q\) are placed with their planes mutually perpendicular with their centers coinciding. The resultant magnetic field induction at the center of the coils is \(\sqrt{x} \, \text{mT}\), where \(x =\) ______.
[Use \(\mu_0 = 4 \pi \times 10^{-7} \, \text{TmA}^{-1}\)]- JEE Main - 2024
- Physics
- Magnetic Field Due To A Current Element, Biot-Savart Law
Given below are two statements
Statement I: Biot-Savart's law gives on the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current carrying conductor only.
Statement II: Biot-Savart’s law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Idl while the latter being produced by a vector source, q.
In light of above statements choose the most appropriate answer from the options given below:- NEET (UG) - 2023
- Physics
- Magnetic Field Due To A Current Element, Biot-Savart Law
Questions Asked in EAMCET exam
- If $\quad \tan \theta \cdot \tan \left(120^{\circ}-\theta\right) \tan \left(120^{\circ}+\theta\right)=\frac{1}{\sqrt{3}}$, then $\theta$ is equal to
- EAMCET - 2015
- Trigonometric Equations
- If $f: R \rightarrow R, g: R \rightarrow R$ are defined by $f(x)=5\, x-3, g(x)=x^{2}+3$, then $g o f^{-1}(3)$ is equal to
- EAMCET - 2015
- Differentiability
- The common roots of the equations $z^{3}+2 z^{2}+2 z+1=0, z^{2014}+z^{2015}+1=0$ are
- EAMCET - 2015
- Quadratic Equations
- The value of the sum $1 \cdot 2 \cdot 3+2 \cdot 3 \cdot 4+3 \cdot 4 \cdot 5+\ldots$ upto $n$ terms is equal to
- EAMCET - 2015
- Sum of First n Terms of an AP
- The system $2\,x+3 y+z=5,3\,x+y+5\,z=7$ and $x+4\,y-2\,z=3$ has
- EAMCET - 2015
- Transpose of a Matrix
Concepts Used:
Biot Savart Law
Biot-Savart’s law is an equation that gives the magnetic field produced due to a current-carrying segment. This segment is taken as a vector quantity known as the current element. In other words, Biot-Savart Law states that if a current carrying conductor of length dl produces a magnetic field dB, the force on another similar current-carrying conductor depends upon the size, orientation and length of the first current carrying element.
The equation of Biot-Savart law is given by,
\(dB = \frac{\mu_0}{4\pi} \frac{Idl sin \theta}{r^2}\)
Application of Biot Savart law
- Biot Savart law is used to evaluate magnetic response at the molecular or atomic level.
- It is used to assess the velocity in aerodynamic theory induced by the vortex line.
Importance of Biot-Savart Law
- Biot-Savart Law is exactly similar to Coulomb's law in electrostatics.
- Biot-Savart Law is relevant for very small conductors to carry current,
- For symmetrical current distribution, Biot-Savart Law is applicable.
For detailed derivation on Biot Savart Law, read more.
SUBSCRIBE TO OUR NEWS LETTER
