The flexible loop in Figure P 31.3 has a radius of 12.0 cm and is in a magnetic field of magnitu

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The flexible loop in Figure P 31.3 has a radius of 12.0 cm...

The flexible loop in Figure $\mathrm{P} 31.3$ has a radius of 12.0 $\mathrm{cm}$ and is in a magnetic field of magnitude 0.150 $\mathrm{T}$ . The loop is grasped at points $A$ and $B$ and stretched until its area is nearly zero. If it takes 0.200 $\mathrm{s}$ to close the loop, what is the magnitude of the average induced emf in it during this time interval?

Key Concepts

Average Induced EMF

The average induced emf is defined as the change in magnetic flux through the loop divided by the time interval over which the change occurs. This concept is important for analyzing situations where the magnetic flux changes gradually, allowing one to compute the emf that is effectively induced over a given period.

Faraday's Law of Electromagnetic Induction

This principle states that an electromotive force (emf) is induced in a closed loop when there is a change in the magnetic flux through the loop. It provides the quantitative relation between the rate of change of the magnetic flux and the induced emf, which is essential for understanding how varying magnetic fields can generate currents in conductive circuits.

Magnetic Flux

Magnetic flux quantifies the amount of magnetic field passing through a given area and is calculated as the product of the magnetic field strength and the area that is perpendicular to the field. It is a critical concept since it directly determines the magnitude of the induced emf in accordance with Faraday's Law when the flux changes over time.

Area Calculation of a Circular Loop

Calculating the area of a circular loop is fundamental when determining the magnetic flux through a loop. The area is computed using the formula A = ?r², where r is the radius of the circle. This calculation is essential for finding the initial flux when the loop is in a magnetic field and for understanding how changes in the loop's geometry affect the flux and, consequently, the induced emf.

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