Certain superconducting magnet in the form of a solenoid of length 0.34 m can generate a magnetic field of 6.5 T in its core when its coils carry a current of 90 A. The windings, made of a niobium-titanium alloy, must be cooled to 4.2 K. Find the number of turns in the solenoid.

The number of turns in the solenoid is 1.95 x 10⁴.

Explanation:

given information:

the length of solenoid, L = 0.34 m

magnetic field, B = 6.5 T

current, I = 90 A

to find the number of turn in solenoid, we can start from the magnetic field equation,

B = μ₀nI, n = N/L

B = magnetic field (T)

μ₀ = permeability (4π × 10⁻⁷ T.m/A)

n = the number turn per unit length (turn/m)

I = current (A)

N = the number turn in solenoid

L = the length of solenoid

thus,

B = μ₀IN/L

N = B L/μ₀I

   = (6.5) (0.34)/(4π × 10⁻⁷) (90)

   = 1.95 x 10⁴ turn

explanation:

v=uf/(u-f)

= 5.-10/(5+10) convex lens has negative focal length

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.