Question 222: Magnetism and Matter

Question

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d > > a).  If the loop  a applies a force F on the wire then :

Accepted Answer

Magnetic field due to current carrying loop at distance d, is,
B  =  $${{{\mu _0}} \over {4\pi }} 	imes {{\overrightarrow M  	imes \overrightarrow d } \over {{d^3}}}$$
=  $${{{\mu _0}} \over {4\pi }} 	imes {{i 	imes \pi {a^2} 	imes d 	imes \sin {{90}^o}} \over {{d^3}}}$$   [as  M = iA]
=  $${{{\mu _0}} \over {4\pi }} 	imes {{i\pi {a^2}} \over {{d^2}}}$$
$$ 	herefore $$   B $$ \propto $$ $${{{a^2}} \over {{d^2}}}$$
We also know,
F = Bil
$$ 	herefore $$   F $$ \propto $$  B
So, F $$ \propto $$  $${{{a^2}} \over {{d^2}}}$$

Answer

$$F = 0$$

Answer

$$F \propto \left( {{a \over d}} \right)$$

Answer

$$F \propto \left( {{{{a^2}} \over {{d^3}}}} \right)$$

Answer

$$F \propto {\left( {{a \over d}} \right)^2}$$

Magnetism and Matter

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d > > a). If the loop a applies a force F on the wire then :

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