Question

if a current is 1.2 a, how many turns per centimeter must be wound on a solenoid in order to produce a magnetic field of 2.0x10⁻³ T within it?

Answer 1

To produce a magnetic field of 2.0x10−3 T with a current of 1.2 A in a solenoid, about 15.92 turns per centimeter are necessary.

Step-by-step explanation:

To determine how many turns per centimeter must be wound on a solenoid to produce a desired magnetic field within it, we use the formula for the magnetic field inside a solenoid, B = μ0nI, where B is the magnetic field, μ0 is the vacuum permeability constant (4π x 10−9 T·m/A), n is the number of turns per meter, and I is the current flowing through the solenoid.

Given the magnetic field B is 2.0x10−3 T and the current I is 1.2 A, solving for n gives us n = B / (μ0I). To convert turns per meter to turns per centimeter, we divide n by 100.

Using the provided information:

1. B = 2.0 x 10−3 T
2. I = 1.2 A
3. μ0 = 4π x 10−9 T·m/A

We obtain:

n = (2.0 x 10−3 T) / (4π x 10−9 T·m/A × 1.2 A)

n = 1591.55 turns per meter

Therefore, the number of turns per centimeter is:

ncm = 1591.55 / 100 = 15.92 turns per centimeter.