The magnetic field due to a current carrying circular loop of radius $$3cm$$ at a point on the axis at a distance of $$4cm$$ from the centre is 54 $$\mu T.$$ What will be its value at the centre of loop?
A.
$$125\mu T$$
B.
$$150\mu T$$
C.
$$250\mu T$$
D.
$$75\mu T$$
Answer :
$$250\mu T$$
Solution :
The magnetic field at a point on the axis of a circular loop at a distance $$x$$ from centre is,
$$\eqalign{
& B = \frac{{{\mu _0}i{a^2}}}{{2{{\left( {{x^2} + {a^2}} \right)}^{\frac{3}{2}}}}}\,\,\,\,B' = \frac{{{\mu _0}i}}{{2a}} \cr
& \therefore B' = \frac{{B.{{\left( {{x^2} + {a^2}} \right)}^{\frac{3}{2}}}}}{{{a^3}}} \cr
& {\text{Put}}\,x = 4\,\& \,a = 3 \Rightarrow B' = \frac{{54\left( {{5^3}} \right)}}{{3 \times 3 \times 3}} = 250\mu T \cr} $$
Releted MCQ Question on Electrostatics and Magnetism >> Magnetic Effect of Current
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