$20 \,A$ current is flowing in a long straight wire. The intensity of magnetic field at a distance of $10\, cm$ from the wire, will be
- $4 \times 10^{-5} Wb / m ^{2}$
- $2 \times 10^{-5} Wb / m ^{2}$
- $3 \times 10^{-5} Wb / m ^{2}$
- $8 \times 10^{-5} Wb / m ^{2}$
The Correct Option is A
Solution and Explanation
$B=\frac{\mu_{0}}{4 \pi} \frac{2 I}{r}$
Given, $I=20\, A$,
$r =10\, cm$
$=10 \times 10^{-2} m$
$\therefore B =10^{-7} \times \frac{2 \times 20}{10 \times 10^{-2}}$
$=4 \times 10^{-5} Wb / m ^{2}$
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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.
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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.