If in a circular coil $$A$$ of radius $$R,$$ current $$I$$ is flowing and in another coil $$B$$ of radius $$2R$$ a current $$2I$$ is flowing, then the ratio of the magnetic fields $${B_A}$$ and $${B_B},$$ produced by them will be
A.
$$1$$
B.
$$2$$
C.
$$\frac{1}{2}$$
D.
$$4$$
Answer :
$$1$$
Solution : KEY CONCEPT : We know that the magnetic field produced by a current carrying circular coil of radius $$r$$ at its centre is $$B = \frac{{{\mu _0}}}{{4\pi }}\frac{I}{r} \times 2\pi \,$$
$$\eqalign{
& {\text{Here}}\,{B_A} = \frac{{{\mu _0}}}{{4\pi }}\frac{I}{R} \times 2\pi \,{\text{and}}\,{B_B} = \frac{{{\mu _0}}}{{4\pi }}\frac{{2I}}{{2R}} \times 2\pi \cr
& \Rightarrow \frac{{{B_A}}}{{{B_B}}} = 1 \cr} $$
Releted MCQ Question on Electrostatics and Magnetism >> Magnetic Effect of Current
Releted Question 1
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