Question:
A horizontal overhead powerline is at height of $4m$ from the ground and carries a current of $100\,A$ from east to west. The magnetic field directly below it on the ground is $\left(\mu_{0} = 4\pi \times10^{-7} Tm A^{-1}\right) $
A horizontal overhead powerline is at height of $4m$ from the ground and carries a current of $100\,A$ from east to west. The magnetic field directly below it on the ground is $\left(\mu_{0} = 4\pi \times10^{-7} Tm A^{-1}\right) $
Updated On: Jan 30, 2025
- $2.5 \times10^{-7} T $ southward
- $5 \times10^{-6} T $ northward
- $5 \times10^{-6} T $ southward
- $2.5 \times10^{-7} T $ northward
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The Correct Option is C
Solution and Explanation
The magnetic field $B = \frac{\mu_{0}}{4\pi} \frac{2I}{r}$
$ = 10^{-7} \times\frac{2\times100}{4} $
$= 5 \times10^{-6} T$
According to right hand palm rule, the magnetic field is directed towards south.
$ = 10^{-7} \times\frac{2\times100}{4} $
$= 5 \times10^{-6} T$
According to right hand palm rule, the magnetic field is directed towards south.
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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.