First slide

Magnetic field due to a straight current carrying wire

Question

A long vertical wire in which a current is flowing produces a neutral point with the earth's magnetic field at a distance of 5 cm from the wire. If the horizontal component of the earth's magnetic induction is 0.18 gauss, then the current in the wire is

Moderate

A

0.45 A
B

4.5 A
C

0.9 A
D

0.036 A

Solution

The magnetic induction B due to current I ampere in a long straight conductor at a distance r metre from it is given by
$\begin{array}{l} B = \frac{μ_{0}}{4 π} \times \frac{2 I}{r} \\ Here, r = 5 cm = 5 \times 10^{- 2} m \\ ∴ B = 10^{- 7} \times \frac{2 \times I}{5 \times 10^{- 2}} = 0 .04 I Gauss \end{array}$
At the neutral point, the magnetic induction due to earth's horizontal component is equal and opposite to that due to current in the conductor.
$∴ 4 I \times 10^{- 2} = 0 .18 or I = 4 .5 A$

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