Two concentric circular loops of radii r₁=30 cm and r₂=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 :

Solution

Physics sir · 3 steps

Each loop has its own moment IA, and the arrows say they point opposite ways, so subtract them.

1. Read the directions. Take x to the right and y up, so k̂ points out of the page. On its right side the inner loop's current goes up, so it runs anticlockwise and its moment is along +k̂. The outer loop's current goes down on its right side, so it runs clockwise and its moment is along -k̂.
2. Size of each moment. Inner loop: μ₁ = Iπ r₁² = 7 × π × 0.09 ≈ 1.98 A m². Outer loop: μ₂ = Iπ r₂² = 7 × π × 0.25 ≈ 5.50 A m².

   μ⃗ₙₑₜ = Iπ(r₁² - r₂²)k̂ = 7π(0.09 - 0.25)k̂ = -1.12π k̂ ≈ -3.52 k̂ A m²

3. So. The bigger, clockwise outer loop wins, and the net moment is about -7/2k̂ A m². That is option (b).

The idea to keep. Magnetic moment is a vector, μ⃗ = I A n, with n from the right-hand rule. Find each loop's direction first, then add the moments as vectors.

Answer from the NTA final answer key. Solution by PrepWiser.