Magnetic field due to currentHard
Question
A battery is connected between two points A and B on the circuimference of a uniform conducting ring of radius r and resistance R. One of the arc AB of the ring substends an angle θ at the centre. The value of the magnetic induction at the centre. The value of the magnetic induction at the centre due to the current in the ring is
Options
A.proportional to (180o - θ)
B.inversely proportional to r
C.zero, only if (θ = 180o)
D.zero for all values of θ
Solution
For a current flowing into a circular arc, the magnetic induction at the centre is
or B ∝ iθ
In the given problem, the toatl current is
divided into two arcs
or iθ = constant
i.e., magnetic field at centre due to arc AB is equal and opposite to the magnetic field at centre due to arc ACB. Or the net magnetic field at centre is zero.
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