A circular loop of radius a=8 cm and carrying a current I2=1A is placed near an infinitely long straight wire carrying a current I1=1Aas shown in the figure. The straight wire and circular loop are coplanar. The distance of the centre of the loop from the wire is b=10 cm. The force of interaction between the straight wire and the loop is nπ3×10-7 N. Find the value of n.

Question

A circular loop of radius a=8 cm and carrying a current I2=1A is placed near an infinitely long straight wire carrying a current I1=1Aas shown in the figure. The straight wire and circular loop are coplanar. The distance of the centre of the loop from the wire is  b=10 cm. The force of interaction between the straight wire and the loop is nπ3×10-7 N. Find the value of n.

Infinity Learn · Accepted Answer

Consider an element on the circular loop at an angle $θ$ with the horizontal. From the symmetry of the figure, only the horizontal component will contribute in net fore. Therefore

$d F = 2 (d F_{1}) \cos θ = 2 (\frac{μ_{0} I_{1}}{2 π (b - a \cos θ)}) (I_{2} a d θ) \cos θ$

$F = \frac{μ_{0} I_{1} I_{2} a}{π} \int_{0}^{π} \frac{\cos θ d θ}{(b - a \cos θ)}$

$\Rightarrow F = μ_{0} I_{1} I_{2} (\frac{b}{\sqrt{b^{2} - a^{2}}} - 1) = 1 \times 4_{π} \times 10^{- 7} (\frac{10}{6} - 1)$

Question Image

Want to Fund your own JEE / NEET / Foundation preparation ??

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!