For the magnetic field to be maximum due to a small
element of current carrying conductor at a point, the
angle between the element and the line joining the
element to the given point must be
- $0^\circ $
- $90^\circ $
- $180^\circ $
- $45^\circ $
The Correct Option is B
Solution and Explanation
The magnetic field due to small element conductor of length is given by
\(dB= \frac{μ_0}{4π}\frac{idl sinθ}{r^2}\)
This value will be maximum when
\(sin\ θ=1=sin\ 90\degree\)
\(θ=90\degree\)
So, the correct answer is (B): 90\(^{\circ}\)
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 BCECE exam
- Instantaneous displacement current of 1.0A in the space between the parallel plates of 1μF capacitor can be established by changing the potential difference of:
- BCECE - 2023
- Electromagnetic waves
- What is the r.m.s value of an alternating current which when passed through a resistor produces heat, which is four times that produced by a current of 2A in the same resistor?
- BCECE - 2023
- Alternating current
- In the displacement method of \(l_1\) and \(l_1\) be the sizes of two images, then the size of the object is:
- BCECE - 2023
- Ray optics and optical instruments
- A beaker is a field with water (μ=\(\frac{4}{3}\)) up to a height of 33.25cm. A concave mirror is placed 15 cm above the water level and the image of an object placed at the bottom is formed 25cm below the water level. The focal length of the mirror is nearly :
- BCECE - 2023
- Ray optics and optical instruments
- An air doubble is inside water (μ=\(\frac{4}{3}\)). At what distance from the air bubble should a point object be placed so as to form a real image at the same distance from the dubble? (r is the radius of curvature of the bubble)
- BCECE - 2023
- Ray optics and optical instruments
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.