A long straight wire of circular cross section of radius a carries asteady current I. The current is uniformly distributed across itscross section. The ratio of the magnitudes of magnetic field at apoint distant a/2 above the surface of wire to that at a point distanta/2 below its surface is(i) 4 :1(ii) 1:1(iii) 4: 3(iv) 3 :4
Question
A long straight wire of circular cross section of radius a carries asteady current I. The current is uniformly distributed across itscross section. The ratio of the magnitudes of magnetic field at apoint distant a/2 above the surface of wire to that at a point distanta/2 below its surface is(i) 4 :1(ii) 1:1(iii) 4: 3(iv) 3 :4
Solution
The magnetic field due to a long straight wire carrying current is symmetrical around the wire. This means that the magnetic field at a point above the wire is the same as at a point below the wire, given that the points are at the same distance from the wire. Therefore, the ratio of the magnitudes of the magnetic field at a point distant a/2 above the surface of the wire to that at a point distant a/2 below its surface is 1:1. So, the correct answer is (ii) 1:1.
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