Magnetic Effects & Magnetism

JEE Main level, single correct, medium

63 of 276

Question 63 of 276

The magnetic field at the centre of a circular coil of radius rr, due to current I flowing through it, is BB. The magnetic field at a point along the axis at a distance r2\dfrac{r}{2} from the centre is :

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Answer: (C) (25)3B{\left(\dfrac{2}{\sqrt{5}}\right)}^{3}B

Magnetic field at the centre of the circle is, B=μ0i2RB=\dfrac{{\mu }_{0}i}{2R}
Magnetic field at the point on the axis is,
B2=μ0iR22(R2+x2)32⇒B2=μ0iR22(R2+(R2)2)32⇒B2=μ0i2(54)32R=(25)3B{B}_{2}=\dfrac{{\mu }_{0}i{R}^{2}}{2{\left({R}^{2}+{x}^{2}\right)}^{\dfrac{3}{2}}}\Rightarrow {B}_{2}=\dfrac{{\mu }_{0}i{R}^{2}}{2{\left({R}^{2}+{\left(\dfrac{R}{2}\right)}^{2}\right)}^{\dfrac{3}{2}}}\Rightarrow {B}_{2}=\dfrac{{\mu }_{0}i}{2{\left(\dfrac{5}{4}\right)}^{\dfrac{3}{2}}R}={\left(\dfrac{2}{\sqrt{5}}\right)}^{3}B

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