## Define Magnetic Flux?

We can define the magnetic flux of a system through a surface area A and it is placed in a uniform magnetic field B as

\(\phi _{B} = B.A = BA Cos\theta\)The \(\theta\) represents the angle between A and B

### Faraday’s Laws of Induction

According to this law, the emf induced in a coil of N turns is in direct proportional to the rate of change of flux through it.

\(\varepsilon \, = -N\frac{\mathrm{d} \phi_{B}}{\mathrm{d} t}\)Here the numerator is the flux associated with only one turn of the coil. When the circuit is closed, a current I=\(\varepsilon\)R is found in it, where R is the resistance of the circuit.

### What is Lenz’s Law?

The lenz’s law states that the polarity of the emf which is induced tends to produce a current opposing to the change in the magnetic flux that produced it. The negative sign represents the opposition.

### Eddy Currents

In nearby metal bodies, changing the magnetic fields can create current loops which get dissipated in the form of heat. These currents are known as eddy current.

### Define Inductance?

Inductance is defined as the ratio between the current and the flux-linkage, which is represented by

\(\varepsilon\)### Important Questions

- If the current carried by the solenoid changes steadily from 4 A to 7 A in 1 s, what is the induced emf in the loop? The solenoid has 30 turns per cm and has a small loop of area 4 cm2 placed inside the solenoid normal to its axis?
- What is the emf developed across the cut if the velocity of the loop is 3 cm s–1 in a direction normal to the loop, longer side, and shorter side.For how long does the induced voltage last in each case if the rectangular wire loop with dimensions of 15 cm and 10 cm with a small cut is moving out of a region of the uniform magnetic field of magnitude 0.5
- If the length of the long metallic rod is 3.0 m and is rotated with an angular frequency of 700 rad s–1 about an axis normal to the rod passing through its one end. Calculate the emf developed between the center and the ring. A circular metallic ring is in contact with the other end of the rod. A constant and uniform magnetic field of 0.10 T parallel to the axis exists everywhere.

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