Question:
The correct plot of the magnitude of magnetic field $\vec{B}$ $vs$ distance $r$ from centre of the wire is, if the radius of wire is $R$
The correct plot of the magnitude of magnetic field $\vec{B}$ $vs$ distance $r$ from centre of the wire is, if the radius of wire is $R$
Updated On: Jul 7, 2022
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The Correct Option is B
Solution and Explanation
The magnetic field from the centre of wire of radius $R$ is given by
$B=\left(\frac{\mu_{0}I}{2R^{2}}\right) r \left(r \,R\right)$
$\Rightarrow B \propto \frac{1}{r}$
From this descriptions, we can say that the graph $\left(b\right)$ is acorrect representation
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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.