Question

The magnetic field due to a current carrying circular loop of radius 3 m at a point on the axis at a distance of 4 m from the centre is $54\mu T$.What will be its value at the centre of the loop?

• A. $250\mu T$
• B. $150\mu T$
• C. $125\mu T$
• D. $75\mu T$

Answer 1

Answer: (A)

$250\mu T$

The magnetic field on the axis of the loop is $B_z=\frac{{\mu }_0}{4\pi }\frac{2\pi R^{2}I}{(z^2+R^2{)}^{3/2}}$

Field at centre is $B_c=\frac{{\mu }_0}{4\pi }\frac{2\pi R^{2}I}{R^3}$

thus, $\frac{B_c}{B_z}=\frac{(z^2+R^2{)}^{3/2}}{R^3}=\frac{(4^2+3^2{)}^{3/2}}{3^3}=\frac{125}{27}$

or $B_c=\frac{125}{27}\times 54=250\mu T$ as $(B_z=54\mu T)$