Question

A solenoid of length 2 m and 6 cm diameter possesses 15 turns per cm. a current of 2a is flowing through it, the magnetic induction at axis inside the solenoid is

A. π×10⁻⁵T
B. 2π×10⁻⁵T
C. 3π×10⁻⁵T
D. 4π×10⁻⁵T

Answer 1

The magnetic induction at the axis inside the solenoid is 3π×10⁻⁵T.

Step-by-step explanation:

To determine the magnetic induction at the axis inside the solenoid, we can use Ampere's Law. Ampere's Law states that the magnetic field inside a long solenoid is proportional to the product of the number of turns per unit length and the current flowing through the solenoid. In this case, the solenoid has a length of 2m and a diameter of 6cm, which means the radius is 3cm. The number of turns per unit length is given as 15 turns per cm, so the total number of turns is 30 turns. The current flowing through the solenoid is 2A.

Using Ampere's Law, we can calculate the magnetic field:

B = μ₀nI

where B is the magnetic field, μ₀ is the permeability of free space (4π×10⁻⁷ Tm/A), n is the number of turns per unit length, and I is the current. Substituting the given values:

B = (4π×10⁻⁷ Tm/A)(15 turns/cm)(2A) = 120π×10⁻⁷ T = 3π×10⁻⁵ T

Therefore, the magnetic induction at the axis inside the solenoid is 3π×10⁻⁵T.