Final answer:
The question deals with Faraday's law of electromagnetic induction applied to a solenoid and a coil. The magnetic flux through the coil is calculated using the product of the solenoid's magnetic field and the coil's area. The induced emf is calculated using the product of the rate of flux change and number of turns.
Step-by-step explanation:
This problem deals with the concept of electromagnetic induction, in specific, Faraday's law of electromagnetic induction. The magnetic field inside the solenoid is given by B = µonI. The magnetic flux through the coil is the product of the solenoid's magnetic field and the area of the coil. Therefore, emf induced in the coil is the product of number of turns and rate change of flux. This means if the current changes in a specific time, there will be an induced emf in the coil.
To find the induced emf in the short coil, we need to calculate the change in magnetic flux through the coil. The magnetic field inside the solenoid is uniform and given by B = µonī, where on is the number of turns per unit length and I is the current. The magnetic flux through the coil is the product of the solenoid's magnetic field and the area of the coil.
The resulting formula will be emf = -N(dϕ/dt), where N is the number of turns and ϕ represents the change in magnetic flux. One must keep in mind that the purpose of the negative sign in Faraday's law highlights the fact that the induced emf and the change in magnetic flux have opposite directions, as noted in Lenz's law.
The solenoid produces the magnetic field, which in turn induces an emf in the tightly wound coil. These principles are key to operation of many types of electrical devices.
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