Question

If a current is 2.1 A, how many turns per centimeter must be wound on a solenoid to produce a magnetic field of 2.5 × 10⁻³ T within it

a) 0.12 turns/cm
b) 0.15 turns/cm
c) 0.18 turns/cm
d) 0.21 turns/cm

Answer 1

To produce a magnetic field of 2.5 × 10⁻³ T with a current of 2.1 A, approximately 0.12 turns per centimeter must be wound on the solenoid.

Step-by-step explanation:

To calculate the number of turns per centimeter needed to produce a magnetic field of 2.5 × 10⁻³ T in a solenoid with a current of 2.1 A, we can use the formula for the magnetic field inside a solenoid:

B = μ₀nI

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 meter
• I is the current

Rearranging the formula to solve for n, we get:

n = B / μ₀I

Substituting the given values:

n = (2.5 × 10⁻³ T) / (4π × 10⁻⁷ T·m/A × 2.1 A) ≈ 0.121 turns/cm

Therefore, the correct answer is option a) 0.12 turns/cm.