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13 Electromagnetism I
13.26 A current I is sent through a thin wire as in Fig. 13.5. The radius of the
curved part of the wire is R. Show that the magnetic induction at the point O
will be B =
μ 0 i
2π R
1 +
3π
4
Fig. 13.5
13.27 (a) A current I is sent through a thin wire as in Fig. 13.6. The straight wires
are very long and the radius of the curved part of the wire is R. Show
that the magnetic induction at the point O will be
B =
μ 0 I (π + 2)
4π R
Fig. 13.6
(b) A wire shown in Fig. 13.7 carries current I . Find the field of induction
B at the centre O.
Fig. 13.7
13.28 (a) A wire in the form of a polygon of n sides is circumscribed by a circle
of radius a. If the current through the wire is i, show that the magnetic
induction at the centre of the circle is given by
B =
μ 0 ni
2πa
tan
π
n
(b) Show that in the limit n → ∞ you get the expected result.