Question 248: Magnetism and Matter

Question

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

Accepted Answer

The magnetic field at a point on the axis of a circular loop at a distance $$x$$ from center is,
$$B = {{{\mu _0}i\,{a^2}} \over {2\left( {{x^2} + {a^2}} ight)3/2}}$$ $$\,\,\,\,\,B' = {{{\mu _0}i} \over {2a}}$$
$$	herefore$$ $$B' = {{B.{{\left( {{x^2} + {a^2}} ight)}^{3/2}}} \over {{a^3}}}$$
Put $$x = 4$$ & $$a = 3 \Rightarrow B' = {{54\left( {{5^3}} ight)} \over {3 	imes 3 	imes 3}} = 250\mu T$$

Answer

$$125\,\mu T$$

Answer

$$150\,\mu T$$

Answer

$$250\,\mu T$$

Answer

$$75\,\mu T$$

Magnetism and Matter

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

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