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Question
A long straight wire of circular cross section of radius 'a' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of magnitudes of the magnetic field at a point `a/2` above the surface of wire to that of a point `a/2` below its surface is ______.
Options
4 : 1
1 : 1
4 : 3
3 : 4
Solution
A long straight wire of circular cross section of radius 'a' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of magnitudes of the magnetic field at a point `a/2` above the surface of wire to that of a point `a/2` below its surface is 4 : 3.
Explanation:
At P2, B2 = `(mu_0I)/(2pi((3a)/2)) = (mu_0I)/(3pia)`
At P1, B1 = `(mu_0(I//4))/(2pi(a//2)) = (mu_0I)/(4pia)`
`therefore B_2/B_1 = (((mu_0I)/(3pia)))/(((mu_0I)/(4pia))) => B_2/B_1 = 4/3`
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