An N -turn square coil with side ℓand resistance R is pulled to the right at constant speed v in

step 1 Given is a n -turn square coil. It has side equals to n and resistance r. It is pulled to the ri

An N -turn square coil with side ℓand resistance R is pulled...

An $N$ -turn square coil with side $\ell$ and resistance $R$ is pulled to the right at constant speed $v$ in the positive $x$ -direction in the presence of a uniform magnetic field $B$ acting perpendicular to the coil, as shown in Figure $\mathrm{P} 20.66 . \mathrm{At} t=0$, the right side of the coil is at the edge of the field. After a time $t$ has elapsed, the entire coil is in the region where $B=0 .$ In terms of the quantities $N, B, \ell$, $v$, and $R$, find symbolic expressions for (a) the magnitude of the induced emf in the loop during the time interval $t_{1}$ (b) the magnitude of the induced current in the coil, (c) the power delivered to the coil, and (d) the force required to remove the coil from the field. (e) What is the direction of the induced current in the loop? What is the direction of the magnetic force on the loop while it is being pulled out of the field?

An $N$ -turn square coil with side $\ell$ and resistance $R$ is pulled to the right at constant speed $v$ in the positive $x$ -direction in the presence of a uniform magnetic field $B$ acting perpendicular to the coil, as shown in Figure $\mathrm{P} 20.66 . \mathrm{At} t=0$, the right side of the coil is at the edge of the field. After a time $t$ has elapsed, the entire coil is in the region where $B=0 .$ In terms of the quantities $N, B, \ell$, $v$, and $R$, find symbolic expressions for (a) the magnitude of the induced emf in the loop during the time interval $t_{1}$
(b) the magnitude of the induced current in the coil,
(c) the power delivered to the coil, and (d) the force required to remove the coil from the field. (e) What is the direction of the induced current in the loop? What is the direction of the magnetic force on the loop while it is being pulled out of the field?

Key Concepts

Magnetic Force on Current-Carrying Conductors

When a current flows through a conductor in a magnetic field, a magnetic force acts on it. This concept explains how induced currents interact with magnetic fields to produce forces, which are essential in determining the mechanical work needed to move conductors in magnetic environments.

Energy Conservation and Power Dissipation

This concept involves analyzing the conversion of mechanical energy into electrical energy, and subsequently into thermal energy due to resistance (Joule heating). It is key to understanding the power delivered to a circuit and the mechanical forces required to overcome electromagnetic damping.

Ohm’s Law

Ohm’s Law relates the voltage, current, and resistance in an electrical circuit. In the context of induced emf, it is used to determine the magnitude of the induced current when the resistance of the circuit is known.

Motional EMF

Motional emf arises when a conductor moves through a magnetic field, leading to a separation of charges and the generation of an emf. This concept directly links mechanical motion with electrical voltage generation and is important for understanding induced currents in moving circuits.

Faraday’s Law of Electromagnetic Induction

This principle states that a changing magnetic flux through a closed loop induces an electromotive force (emf) in that loop. It is fundamental for understanding how motion in a magnetic field or a time-varying magnetic field generates electrical potentials in conductors.

Lenz’s Law

Lenz’s Law explains that the direction of the induced emf and current is such that the magnetic field created by the induced current opposes the change in the original magnetic flux. This concept is crucial for predicting the oppositional nature of induced effects in electromagnetic systems.

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