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Question:

A Helmholtz coil has a pair of loops, each with N turns and radius R. They are placed coaxially at distance R, and the same current I flows through the loops in the same direction. The magnitude of the magnetic field at P, midway between the centers A and C, is given by (Refer to figure):

4Nμ₀I5³/²R

8Nμ₀I5¹/²R

8Nμ₀I5³/²R

4Nμ₀I5¹/²R

Solution:

The magnetic field due to both the coils are in the same direction and equal in magnitude.
The magnitude of the magnetic field due to one coil is given as:
B = μ₀iR²/2(R² + (R/2)²)³/²
B = 4μ₀iR²/5√5R²
Bnet = 2B
Bnet = 8μ₀iR²/5√5R²
The correct option is 8Nμ₀I5³/²R