A steady current is flowing in a circular coil of radius $$R,$$ made up of a thin conducting wire. The magnetic field at the center of the loop is $${B_L}.$$ Now,
a circular loop of radius $$\frac{R}{n}$$ is made form the same wire without changing its length, by unfolding and refolding the loop, and the same current is
passed through it. If new magnetic field at the centre of the coil is $${B_C},$$ then the ratio $$\frac{{{B_L}}}{{{B_C}}}$$ is
A.
$$1:{n^2}$$
B.
$${n^{\frac{1}{2}}}$$
C.
$$n:1$$
D.
None of these
Answer :
$$1:{n^2}$$
Solution :
$${B_L} = \frac{{{\mu _0}I}}{{2\pi R}}$$
If the radius is $$\frac{R}{n};$$ the number of turns will be $$n.$$
$$\eqalign{
& {B_C} = \frac{{n{\mu _0}I}}{{2\pi \left( {\frac{R}{n}} \right)}} = {n^2}\frac{{{\mu _0}I}}{{2\pi R}} \cr
& {\text{Hence,}}\,\,\frac{{{B_L}}}{{{B_C}}} = \frac{1}{{{n^2}}} \cr} $$
Releted MCQ Question on Electrostatics and Magnetism >> Magnetic Effect of Current
Releted Question 1
A conducting circular loop of radius $$r$$ carries a constant current $$i.$$ It is placed in a uniform magnetic field $${{\vec B}_0}$$ such that $${{\vec B}_0}$$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is
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 arcs $$AB$$ of the ring subtends an angle $$\theta $$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is
A.
proportional to $$2\left( {{{180}^ \circ } - \theta } \right)$$
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