13.2 Problems
589
13.29 A wire of length l can form a circle or a square. A current i is set up in both
the structures. Show that the ratio of magnetic induction at the centres of
these structures will be approximately 0.87.
13.30 (a) C is the common centre of the circular arcs of the circuit-carrying current
i, its arcs cutting a sector of angle, θ . Show that the magnetic induction
at C is
B =
μ 0 iθ
4π
1
R 1
−
1
R 2
(b) C is the common centre of the semicircular arc of radii R 1 and R 2 ,
Fig. 13.8, carrying current i. Show that the magnetic induction at C is
B =
μ 0 i
4
1
R 1
−
1
R 2
Fig. 13.8
13.31 A long wire is bent into the shape as in Fig. 13.9, without any cross-contact
at P. The current flows as indicated with the circular portion having radius
R. Show that the magnetic induction at C, the centre of the circle is B =
μ 0 i
2R
1 +
1
π
Fig. 13.9
13.32 A current I flows through a ring of radius r placed in the xy-plane. Show that
the magnetic induction at a point along the z-axis passing through the centre
of the ring is given by
B(z) =
μ 0 I R 2
2(R 2 + z 2 ) 3/2
13.33 Five hundred turns of a wire are wound on a thin tube 1 m long. If the wire
carries a current of 5 A, determine the field in the tube.
13.34 Two parallel wires, a distance d apart, carry equal currents I in opposite
directions. Calculate the magnetic induction B for points between the wires
at a distance x from one wire.
[Adapted from Hyderabad Central University 1993]
589
13.29 A wire of length l can form a circle or a square. A current i is set up in both
the structures. Show that the ratio of magnetic induction at the centres of
these structures will be approximately 0.87.
13.30 (a) C is the common centre of the circular arcs of the circuit-carrying current
i, its arcs cutting a sector of angle, θ . Show that the magnetic induction
at C is
B =
μ 0 iθ
4π
1
R 1
−
1
R 2
(b) C is the common centre of the semicircular arc of radii R 1 and R 2 ,
Fig. 13.8, carrying current i. Show that the magnetic induction at C is
B =
μ 0 i
4
1
R 1
−
1
R 2
Fig. 13.8
13.31 A long wire is bent into the shape as in Fig. 13.9, without any cross-contact
at P. The current flows as indicated with the circular portion having radius
R. Show that the magnetic induction at C, the centre of the circle is B =
μ 0 i
2R
1 +
1
π
Fig. 13.9
13.32 A current I flows through a ring of radius r placed in the xy-plane. Show that
the magnetic induction at a point along the z-axis passing through the centre
of the ring is given by
B(z) =
μ 0 I R 2
2(R 2 + z 2 ) 3/2
13.33 Five hundred turns of a wire are wound on a thin tube 1 m long. If the wire
carries a current of 5 A, determine the field in the tube.
13.34 Two parallel wires, a distance d apart, carry equal currents I in opposite
directions. Calculate the magnetic induction B for points between the wires
at a distance x from one wire.
[Adapted from Hyderabad Central University 1993]