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A solenoid 4 cm in diameter and 20 CM in length has 250 turns and carries a current of 15 ampere calculate the flux through the surface of a disc of 10 cm radius that is positioned perpendicular to and centred on the axis of the solenoid?
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**Calculation of Magnetic Field Inside the Solenoid**

To calculate the flux through the surface of the disc, we first need to calculate the magnetic field inside the solenoid. The magnetic field inside a solenoid can be calculated using the formula:

B = μ₀ * n * I

Where:
B is the magnetic field
μ₀ is the permeability of free space (4π × 10^-7 T·m/A)
n is the number of turns per unit length
I is the current flowing through the solenoid

Given that the solenoid has a diameter of 4 cm and a length of 20 cm, we can calculate the number of turns per unit length (n) using the formula:

n = N / L

Where:
N is the total number of turns
L is the length of the solenoid

Substituting the given values, we get:

n = 250 / 0.2 = 1250 turns/m

Now we can calculate the magnetic field inside the solenoid:

B = (4π × 10^-7 T·m/A) * (1250 turns/m) * (15 A) = 7.5π × 10^-4 T

**Calculation of Flux through the Disc**

To calculate the flux through the surface of the disc, we can use the formula:

Φ = B * A

Where:
Φ is the magnetic flux
B is the magnetic field
A is the area of the disc

Given that the radius of the disc is 10 cm, the area of the disc can be calculated using the formula:

A = π * r²

Substituting the given value, we get:

A = π * (0.1 m)² = 0.01π m²

Now we can calculate the flux through the disc:

Φ = (7.5π × 10^-4 T) * (0.01π m²) = 7.5 × 10^-6 Wb

Therefore, the flux through the surface of the disc is 7.5 × 10^-6 Weber.
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A solenoid 4 cm in diameter and 20 CM in length has 250 turns and carries a current of 15 ampere calculate the flux through the surface of a disc of 10 cm radius that is positioned perpendicular to and centred on the axis of the solenoid?
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