A 30-turn circular coil of radius 4.00 cm and resistance...

A 30-turn circular coil of radius $4.00 \mathrm{~cm}$ and resistance $1.00 \Omega$ is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression $B=0.0100 t+0.0400 t^{2}$, where $t$ is in seconds and $B$ is in tesla. Calculate the induced emf in the coil at $t=5.00 \mathrm{~s} .$

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Key Concepts

Faraday's Law of Electromagnetic Induction

Faraday's law states that a changing magnetic flux through a closed loop induces an electromotive force (emf) in the loop. The induced emf is proportional to the negative rate of change of magnetic flux over time, which forms the basis for understanding how varying magnetic fields can generate electric currents in circuits.

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetic field passing through a given area. It is defined as the product of the magnetic field component perpendicular to the surface and the area of the surface. Understanding magnetic flux is essential because its rate of change determines the magnitude of the induced emf according to Faraday's law.

Effect of Coil Turns

When a coil has multiple turns, the total induced emf is the sum of the emf induced in each individual loop. This means that the net induced emf is obtained by multiplying the emf from one loop by the total number of turns, highlighting the significance of coil geometry in electromagnetic induction.

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