A coil in the shape of an equilateral triangl | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The area of an equilateral triangle with side length $a = 10 \, cm = 0.1 \, m$ is given by $A = \frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{3}}{4} (0.1)^

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) The area of an equilateral triangle with side length $a = 10 \, cm = 0.1 \, m$ is given by $A = \frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{3}}{4} (0.1)^2 = \frac{\sqrt{3}}{4} 	imes 0.01 \, m^2$.The magnetic moment of the coil is $M = I A = 0.2 	imes \frac{\sqrt{3}}{4} 	imes 0.01 = 0.05 	imes \sqrt{3} 	imes 0.01 = 5 \sqrt{3} 	imes 10^{-4} \, Am^2$.The torque acting on the coil is $	au = M B \sin 	heta$,where $	heta$ is the angle between the normal to the coil and the magnetic field. When the plane of the coil is parallel to the magnetic field,the normal to the coil is perpendicular to the magnetic field,so $	heta = 90^{\circ}$.Thus,$	au = M B \sin 90^{\circ} = M B = (5 \sqrt{3} 	imes 10^{-4}) 	imes (20 	imes 10^{-3} \, T) = 100 \sqrt{3} 	imes 10^{-7} = \sqrt{3} 	imes 10^{-5} \, Nm$.Comparing this with $\sqrt{x} 	imes 10^{-5} \, Nm$,we get $\sqrt{x} = \sqrt{3}$,which implies $x = 3$.

Similar Questions

Four wires each of length $2.0 \, m$ are bent into four loops $P$,$Q$,$R$ (labeled as $P$ in the image,but distinct),and $S$ and then suspended in a uniform magnetic field. The same current is passed through each loop. Which statement is correct?

Two similar wires of equal lengths are bent in the form of a square and a circular loop. They are suspended in a uniform magnetic field and the same current is passed through them. The torque experienced by:

The torque required to hold a small circular coil of $10$ turns, area $1 \,mm^{2}$ and carrying a current of $\left(\frac{21}{44}\right) \,A$ in the middle of a long solenoid of $10^{3} \,turns/m$ carrying a current of $2.5 \,A$, with its axis perpendicular to the axis of the solenoid is

Write an expression for the torque acting on a current-carrying loop suspended in a uniform magnetic field.

Vedclass Test Series

Exam Paper Generator

Online Exam Module