Two concentric circular loops of radii \(r_1 = 30\) cm and \(r_2 = 50\) cm are placed in \(X–Y\) plane as shown in the figure. \(A\) current \(I = 7 \;A\) is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately
- \(\frac{7}{2}\hat k\; Am^2\)
- \(-\frac{7}{2}\hat k\;Am^2\)
- \(7\hat k\;Am^2\)
- \(-7\hat k\;Am^2\)
The Correct Option is B
Solution and Explanation
The net magnetic moment of this system of two circular loops is :
\(μ_1 = πr^2_1 \times I_1\)
\(μ_2 = πr^2_2 \times I_2\)
Hence,\(μ_{net} = (μ_2-μ_1)(-\hat k)\)
= \(π(r^2_2-r^2_1)I(-\hat k)\)
= \(3.142 \times (0.5^2-03^2)\times 7(-\hat k)\)
= \(- \frac{7}{2}\hat k \;Am^2\)
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Concepts Used:
Electromagnetic Induction
Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-
- When we place the conductor in a changing magnetic field.
- When the conductor constantly moves in a stationary field.
Formula:
The electromagnetic induction is mathematically represented as:-
e=N × d∅.dt
Where
- e = induced voltage
- N = number of turns in the coil
- Φ = Magnetic flux (This is the amount of magnetic field present on the surface)
- t = time
Applications of Electromagnetic Induction
- Electromagnetic induction in AC generator
- Electrical Transformers
- Magnetic Flow Meter