Electromagnetic Induction

Motional EMF is a condition which arises due to the movement of conductor in a magnetic field. On the other hand, induced EMF is a cause of change in the magnetic fiedl over a certain timespan. Induced EMF arises when there is a change in the magnetic flux.

The movement of the body in the conductor is caused by the magnetic field. This magnetic field then causes an electric current to flow in the system. Hence, the direct action is caused by the magnetic force on the object, due to which it becomes the major source of motional EMF.

This negative sign is a result of the derivation of Lenz's law, which is used to signify the principle of conservation of energy. As per this law, the EMF always opposes the flow of magnetic flux in a circuit. And if this doesn't happen, the fundamental laws and theories of physics can be proved wrong by changing the magnetic flux.

Galvanometer is a device having low resistance which is used to detect tiny bits of electric current scattered among different directions in the circuit. Whereas, a voltmeter is used to calculate the potential difference between two different points in the circuit. A galvanometer can also be used as a voltmeter if connected to high resistance in a series.

They core difference between these two terms lies in the fact that self induction involves only one coil as compared to mutual induction involving two. In mutual induction, the change of electric current in one coil produces a magnetic field which results in generating EMF in the second coil. Whereas there is no concept of neighbouring coil in self induction and everything happens within the one coil itself.

$L\frac{di}{dt}=V\Rightarrow 2di=3tdt\Rightarrow 2{\displaystyle \underset{0}{\overset{i}{\int }}di=3}{\displaystyle \underset{0}{\overset{4}{\int }}tdt\Rightarrow i=12A}$

$U=\frac{1}{2}L{i}^2=\frac{1}{2}*2*12^2=144J$

$L\frac{di}{dt}=V?2di=3tdt?2{\displaystyle \underset{0}{\overset{i}{?}}di=3}{\displaystyle \underset{0}{\overset{4}{?}}tdt?i=12A}$

$U=\frac{1}{2}L{i}^2=\frac{1}{2}*2*12^2=144J$

$V=\frac{-d?}{dt}=-\left(15t^2+8t+2\right)$

at t = 2 sec, V = - (15 * 4 + 8 * 2 + 2)

 = 78 V

$I=\frac{V}{R}=\frac{78}{5}=15.6A$

$Q=\Delta \upsilon +w\Rightarrow nC\Delta T=n{C}_v\Delta T=\frac{nC\Delta T}{4}=\frac{3}{4}nC\Delta T=n{C}_v\Delta T$

$C=\frac{4}{3}{C}_v=\frac{4}{3}*\frac{3}{2}R=2R$