Magnetics 2 Question 16

16. A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcsAB of the ring subtends an angle θ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

(1995,2M)

(a) proportional to (180θ)

(b) inversely proportional to r

(c) zero, only if (θ=180)

(d) zero for all values of θ

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Answer:

Correct Answer: 16. (c)

Solution:

  1. For a current flowing into a circular arc, the magnetic induction at the centre is

B=μ0i4πrθ or Biθ

In the given problem, the total current is divided into two arcs

i1 resistance of arc 1 length of arc 1 angle subtended at centre (θ)iθ= constant 

or

i.e. magnetic field at centre due to arcAB is equal and opposite to the magnetic field at centre due to arcACB. Or the net magnetic field at centre is zero.



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