Question

An equilateral triangle of side l is formed from a piece of wire of uniform resistance. The current i is fed as shown in the figure. The magnitude of the magnetic field at its centre O is ______.

पर्याय

• `(sqrt3mu_0"i")/(2pi"l")`

• `(3sqrt3mu_0"i")/(2pi"l")`

• `(mu_0"i")/(2pi"l")`

• zero

Answer 1

An equilateral triangle of side l is formed from a piece of wire of uniform resistance. The current i is fed as shown in the figure. The magnitude of the magnetic field at its centre O is zero.

Explanation:

B₁ = `mu_0/(4pi)(2"i"//3)/"r"`   [sin 30° + sin 30°]

= `mu_0/(4pi)(2"i")/(3"r")`

It is directed outside the paper. Magnetic field at O, due to PQR (i. e., for the wire PQ and QR)

B₂ = `2xxmu_0/(4pi)(("i"/3))/mu`   [sin 30° + sin 30°]

= `mu_0/(4pi)(2"i")/(3"r")`

It is directed inside the paper.

∴ Resultant magnetic field at O

B = B₁​ − B₂ ​= 0