Q23 of 92 Page 249

Find the magnetic field B at the centre of a rectangular loop of length ℓ and width b, carrying a current i.

Let us consider two angles made by points A and B with point O be θ1 and θ2 respectively.


θ1 = θ2 = θ


Let distance of the point from the wire



In triangle




Thus induced magnetic field due to AB is given by,



⇒


⇒


⇒


Similarly the induced magnetic field due to current in BC is given as:



Now, magnetic field due to CD = magnetic field due to current in wire AB =B


Also, magnetic field due to current in wire DA = magnetic field due to current in wire BC =B’


∴





More from this chapter

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21

A wire of length ℓ is bent in the form of an equilateral triangle and carries an electric current i. (a) Find the magnetic field B at the centre.

(b) If the wire is bent in the form of a square, what would be the value of B at the centre?


 22

A very long wire carrying a current i is bent to form a plane at an angle α. Find the magnetic field B at a point P on the bisector of this angle situated at a distance x from the vertex A.

 24

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.


 25

Each of the batteries shown in figure has an emf 5V. Prove that the magnetic field B at the point P is zero for any set of values of the resistances.