Here are the essential concepts you must grasp in order to answer the question correctly.
Faraday's Law of Electromagnetic Induction
Faraday's Law states that a change in magnetic flux through a closed loop induces an electromotive force (emf) in that loop. The induced emf is proportional to the rate of change of the magnetic flux, which is the product of the magnetic field strength and the area through which it passes. This principle is fundamental in understanding how changing magnetic fields can generate electric currents.
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Magnetic Flux
Magnetic flux is a measure of the quantity of magnetism, taking into account the strength and the extent of a magnetic field. It is defined as the product of the magnetic field (B) and the area (A) perpendicular to the field through which it passes, expressed as Φ = B · A. In the context of the solenoid, the flux changes as the magnetic field strength increases, which is crucial for calculating the induced emf.
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Induced EMF in a Loop
The induced emf in a circular loop placed in a varying magnetic field can be calculated using the formula ε = -dΦ/dt, where ε is the induced emf and dΦ/dt is the rate of change of magnetic flux through the loop. For a loop of radius R/2 centered on the axis of a solenoid, the area and the magnetic field strength at that radius must be considered to determine the magnitude of the induced emf accurately.
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