A long wire carries a current of 3.0A along the central axis of a long solenoid (radius=3.0cm, n=900 turns per meter, current=30.0mA). What is the magnitude of the magnetic field at a point 2.0cm from the axis of the solenoid (neglecting any end effects)?

B = 63.93 μT

Explanation:

Current carried by the wire, I₁ = 3.0 A

Number of turns, n = 900 turns/ meter

Radius of the solenoid, R = 3 cm = 0.03 m

r = 2 cm = 0.02 m

Current due to the solenoid, I₂ = 30 mA = 0.03 A

The magnetic field is due to the current carrying conductor and the solenoid

Magnetic field due to the current carrying conductor:

Magnetic field due to the solenoid:

Add B₁ and B₂ together

B = B₁ and B₂

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.