A 500 turn solenoid with a length of 20 cm and a radius of 1.5 cm carries a current of 2.0 A. A second coil of four turns is wrapped tightly about this solenoid so that it can be considered to have the same radius as the solenoid. Find the following when the current in the solenoid increases to 5.0 A in a period of 0.90 s.
(a) the change in the magnetic flux through the coil
T·m2
(b) the magnitude of the average induced emf in the coil
V
a. B=mu*N*i
dB/dt=mu*N*di/dt
b. apply Faraday's equation
So i use B=mu*N*i to find a than what does dB/dt=mu*N*di/dt mean?
To find the change in magnetic flux through the coil and the magnitude of the average induced emf, we can follow these steps:
Step 1: Calculate the initial magnetic flux through the coil.
The magnetic flux through a solenoid can be calculated using the formula:
Φ = μ₀ * n * A * I
Where:
Φ is the magnetic flux
μ₀ is the permeability of free space (a constant)
n is the number of turns per unit length
A is the cross-sectional area of the solenoid
I is the current
For the solenoid, we have:
n = 500 turns / (length of solenoid) = 500 / 0.20 m = 2500 turns/m
A = π * (radius of solenoid)² = π * (0.015 m)²
Plugging in the values, we can calculate the initial magnetic flux through the coil.
Step 2: Calculate the final magnetic flux through the coil.
When the current in the solenoid increases, the magnetic flux through the coil changes. The change in magnetic flux is given by:
ΔΦ = μ₀ * n * A * ΔI
Where:
ΔΦ is the change in magnetic flux
ΔI is the change in current
We are given that the current changes from 2.0 A to 5.0 A. Therefore, we can calculate the change in magnetic flux.
Step 3: Calculate the change in flux and the average induced emf in the coil.
(a) The change in magnetic flux through the coil is the same as the change in magnetic flux through the solenoid. So, the answer to part (a) is the same as the change in magnetic flux we calculated in Step 2.
(b) The average induced emf in the coil can be calculated using Faraday's law:
ε = -N * (ΔΦ/Δt)
Where:
ε is the induced emf
N is the number of turns in the secondary coil
ΔΦ is the change in magnetic flux through the coil
Δt is the time taken for the current to change
We are given that the secondary coil has 4 turns. Therefore, plugging in the values, we can calculate the average induced emf in the coil.
By following these steps and using the given values, you can find the answers to part (a) and part (b) of the question.