A coil of radius 16cm is to produce a magnetic field of 2.4×10^-5 at the center, find the number of turns if a current of 0.5 passed through it. A.12 B.9 C.45 D.18 E.24?

All_for_one

2 years ago

The formula to calculate the magnetic field at the center of a coil is given by:

B = (μ₀ * N * I) / (2 * R)

Where:
B is the magnetic field (2.4 x 10^-5 T in this case)
μ₀ is the permeability of free space (4π x 10^-7 T·m/A)
N is the number of turns
I is the current (0.5 A in this case)
R is the radius of the coil (16 cm, or 0.16 m when converted to meters)

Let's solve for N:

2.4 x 10^-5 = (4π x 10^-7 * N * 0.5) / (2 * 0.16)

Now, we can calculate N:

N = (2.4 x 10^-5 * 2 * 0.16) / (4π x 10^-7 * 0.5)

N ≈ 12

So, the number of turns is approximately 12, which matches option A.