3. A long Solenoid with n=900.0 turns/m has a radius of 10.0 cm. This solenoid is 1.2 m long, and the wire resistance is R = 2.402. This solenoid is immerse it in a non-uniform magnetic field parallel to its axis, with its value changing with a frequency of f-60 Hz, given by B = (5.0 Cosat)/r, where r is the distance measured from the central axis of the solenoid. a) Calculate the flux of this B-filed through the solenoid as a function of time. (Hint: since the B field is non-uniform, you need to do an integration to find the flux, by first dividing the cross section of the solenoid into thin rings.) b) Use the Faraday's law of induction to determine the generated current is in the solenoid. (At this time, the two ends of the solenoid wire are connected to form a closed circuit). c) Write down an expression for the magnitude of the electric filed inside the solenoid wire.
3. A long Solenoid with n=900.0 turns/m has a radius of 10.0 cm. This solenoid is 1.2 m long, and the wire resistance is R = 2.402. This solenoid is immerse it in a non-uniform magnetic field parallel to its axis, with its value changing with a frequency of f-60 Hz, given by B = (5.0 Cosat)/r, where r is the distance measured from the central axis of the solenoid. a) Calculate the flux of this B-filed through the solenoid as a function of time. (Hint: since the B field is non-uniform, you need to do an integration to find the flux, by first dividing the cross section of the solenoid into thin rings.) b) Use the Faraday's law of induction to determine the generated current is in the solenoid. (At this time, the two ends of the solenoid wire are connected to form a closed circuit). c) Write down an expression for the magnitude of the electric filed inside the solenoid wire.
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![### Problem 3: Solenoid in a Non-Uniform Magnetic Field
A long solenoid with specifications:
- Number of turns per meter: \( n = 900.0 \, \text{turns/m} \)
- Radius: \( 10.0 \, \text{cm} \)
- Length: \( 1.2 \, \text{m} \)
- Wire resistance: \( R = 2.4 \, \Omega \)
This solenoid is immersed in a non-uniform magnetic field parallel to its axis. The magnetic field changes with a frequency of \( f = 60 \, \text{Hz} \), and is given by the equation:
\[ B = \frac{5.0 \, \text{cos}(\omega t)}{r} \]
where \( r \) is the distance from the central axis of the solenoid.
**Tasks:**
a) **Calculate the Magnetic Flux**
Determine the flux of the magnetic field through the solenoid as a function of time. *(Hint: Since the magnetic field is non-uniform, integration is required. Begin by dividing the solenoid’s cross-sectional area into thin rings.)*
b) **Apply Faraday’s Law of Induction**
Use Faraday’s law to find the current generated in the solenoid. *(Note: Assume the solenoid forms a closed circuit during this process.)*
c) **Expression for Electric Field Magnitude**
Derive an expression for the magnitude of the electric filed inside the solenoid wire.
d) **Energy Storage**
Calculate the energy stored in the solenoid as a function of time and discuss its nature.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6938446-18ef-4c60-abd7-f53d469db873%2F0de430c1-a8f1-4611-bfc4-454e19af5a0e%2Flyf6tin_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 3: Solenoid in a Non-Uniform Magnetic Field
A long solenoid with specifications:
- Number of turns per meter: \( n = 900.0 \, \text{turns/m} \)
- Radius: \( 10.0 \, \text{cm} \)
- Length: \( 1.2 \, \text{m} \)
- Wire resistance: \( R = 2.4 \, \Omega \)
This solenoid is immersed in a non-uniform magnetic field parallel to its axis. The magnetic field changes with a frequency of \( f = 60 \, \text{Hz} \), and is given by the equation:
\[ B = \frac{5.0 \, \text{cos}(\omega t)}{r} \]
where \( r \) is the distance from the central axis of the solenoid.
**Tasks:**
a) **Calculate the Magnetic Flux**
Determine the flux of the magnetic field through the solenoid as a function of time. *(Hint: Since the magnetic field is non-uniform, integration is required. Begin by dividing the solenoid’s cross-sectional area into thin rings.)*
b) **Apply Faraday’s Law of Induction**
Use Faraday’s law to find the current generated in the solenoid. *(Note: Assume the solenoid forms a closed circuit during this process.)*
c) **Expression for Electric Field Magnitude**
Derive an expression for the magnitude of the electric filed inside the solenoid wire.
d) **Energy Storage**
Calculate the energy stored in the solenoid as a function of time and discuss its nature.
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