Induced current in a coil around a solenoid

In summary, the problem involves a coil with 150 turns and a solenoid with 300 turns/cm. The current in the solenoid changes from 0 to 1.8 A in 0.12 s. The magnetic field generated by the solenoid is calculated using B=μ*n*I(t), and the induced emf in the coil is found using d(BA)/dt. However, the calculated induced current of 0.000093 A is incorrect, and the mistake is unknown.
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Homework Statement



A coil with 150 turns, a radius of 5.0 cm, and a resistance of 12 Ω surrounds a solenoid with 300 turns/cm and a radius of 4.3cm; see the figure. The current in the solenoid changes at a constant rate from 0 to 1.8 A in 0.12 s.

Homework Equations



B from solenoid = μ*n*I(t)
Induced emf = d(BA)/dt

The Attempt at a Solution



First I found the magnetic field generated by the solenoid as a function of time:

B(t) = (1.8/.12)*μ*n*t

Then found induced emf in the coil using d(B[itex]_{solenoid}[/itex]*A[itex]_{coil}[/itex])/d(t)

Then divided that result by the coil's resistance to get induced current, which I found to be .000093 A. However, this is wrong and I'm not sure where I'm making a mistake.

Thanks
 

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  • #2
PS - I'm using n = 30000 turns/m since n is originally given in turns/cm
 

1. What is an induced current in a coil around a solenoid?

An induced current in a coil around a solenoid is an electrical current that is created through electromagnetic induction. This occurs when there is a change in the magnetic field within the solenoid, which then induces a current in the coil surrounding it.

2. How is an induced current created in a coil around a solenoid?

An induced current is created in a coil around a solenoid through Faraday's Law of Electromagnetic Induction. This law states that a changing magnetic field will induce an electric current in a closed loop, such as a coil, surrounding the changing magnetic field.

3. What factors affect the strength of the induced current in a coil around a solenoid?

The strength of the induced current in a coil around a solenoid is affected by several factors, including the strength of the magnetic field, the number of turns in the coil, the rate of change of the magnetic field, and the resistance of the coil.

4. How does the direction of the induced current in a coil around a solenoid relate to the direction of the changing magnetic field?

The direction of the induced current in a coil around a solenoid is determined by the direction of the changing magnetic field. This is known as Lenz's Law, which states that the induced current will flow in a direction that opposes the change in the magnetic field that caused it.

5. What are some practical applications of induced current in a coil around a solenoid?

Induced current in a coil around a solenoid has many practical applications, such as in generators, transformers, and electric motors. It is also used in devices like metal detectors and magnetic resonance imaging (MRI) machines. Additionally, it is used in wireless charging technology and induction cooking.

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