Calculating the Number of Turns in a Solenoid
A 35.0-cm long solenoid 1.25 cm in diameter is to produce a field of 0.390 T at its center.
Explanation:
The question is asking about a solenoid, which is a device used to create a magnetic field when an electric current flows through it. The given information states that the solenoid is 35.0 cm long and 1.25 cm in diameter, and it needs to produce a magnetic field of 0.390 T at its center. To calculate the number of turns required for the solenoid, we can use the formula: B = μ₀ni, where B is the magnetic field, μ₀ is the permeability of free space, n is the number of turns per unit length, and i is the current through the solenoid.
Calculating the Number of Turns:
To calculate the number of turns required for the solenoid in order to produce the desired magnetic field at its center, you can use the formula B = μ₀ni. This formula relates the magnetic field (B) to the permeability of free space (μ₀), the number of turns per unit length (n), and the current through the solenoid (i). By rearranging the formula and substituting the given values, you can find the number of turns per unit length and then calculate the total number of turns needed for the solenoid.
Calculating the Total Number of Turns:
After finding the number of turns per unit length, we can multiply it by the length of the solenoid to calculate the total number of turns required for the solenoid.
How can the number of turns required for the solenoid be calculated? The number of turns required for the solenoid can be calculated using the formula B = μ₀ni, where B is the magnetic field, μ₀ is the permeability of free space, n is the number of turns per unit length, and i is the current through the solenoid.