Q. 244.0( 3 Votes )
A polygon of n equal sides is formed by bending a current carrying wire to total length 2πr which carries a current i.
(a) Find the magnetic field B at the center of the n-sided polygon.
(b) By letting n → ∞, derive the expression for the induced magnetic field at the center of a circular current carrying wire.
Answer :
a) Using the diagram,
For a polygon of n equal sides, the angle at the centre is .
⇒
Considering angle to be very small
Using Biot–Savart’s law for one side of the n-sided polygon,
⇒
(substituting the value of r)
(substituting the value of l)
For n-sided polygon
B’ =nB
⇒
b) When n → ∞, polygon tends to a circle with radius r and magnetic field will tend toward
Rate this question :






















Two proton beams going in the same direction repel each other whereas tow wires carrying currents in the same direction attract each other. Explain.
HC Verma - Concepts of Physics Part 2Consider the situation described in the previous problem. Suppose the current i enters the loop at the point A and leaves it at the point B. Find the magnetic field at the centre of the loop.
HC Verma - Concepts of Physics Part 2Consider the situation shown in figure. The straight wire is fixed but the loop can move under magnetic force. The loop will
HC Verma - Concepts of Physics Part 2
Find the magnetic field B at the centre of a rectangular loop of length ℓ and width b, carrying a current i.
HC Verma - Concepts of Physics Part 2