Question:

Two parallel long wires A and B carry currents $i_1$ and $i_2 (< i_1)$. When $i_1$ and $i_2$ are in the same direction, the magnetic field at a point mid way between the wires is $10 \,\mu\,T$. If $i_2$ is reverse the field becomes $30\, \mu T$. The ratio $i_1/i_2$ is

Updated On: Aug 1, 2022
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The Correct Option is B

Solution and Explanation

$\frac{\mu_{0}}{4\pi} \frac{2i_{1}}{r}-\frac{\mu_{0}}{4\pi} \frac{2i_{2}}{r}=10 \mu T$ $\frac{\mu _{0}}{4\pi }\frac{2i_{1}}{r}+\frac{\mu _{0}}{4\pi } \frac{2i_{2}}{r}=30 \mu T$ On solving $i_{1} = 20 A and i_{2} = 10 A. ? i_{1}/i_{2} = 2$
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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.