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

Question

Infinity Learn · Accepted Answer

The magnetic induction B due to current I ampere in a long straight conductor at a distance r metre from it is given $$byB=$$μ$$04$$π ×  $$2IrHere$$,  $$r=5$$  cm $$=$$ $$5$$  ×  $$10$$−$$2$$ m∴    $$B=10$$−$$7$$ ×  $$2$$ × $$I5$$ × $$10$$−$$2=$$  $$0$$ $$.04$$ I  Gauss 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.∴     $$4I$$  ×  $$10$$−$$2$$ $$=$$  $$0.18$$  or  I  $$=$$  $$4.5$$  A

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

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