Question
Explain mutual induction using Faraday's two coil experiment. Obtain expression
✓
Answer
$\varepsilon_1=- M \frac{d l_2}{d t}$.
→In the figure, arrangement of two coil experiment is shown. Here, coils $C _1$ and $C _2$ are placed coaxially.
→When electric current $I _2$ passing through coil $C _2$ changes, magnetic flux linked with coil $C _1$ changes and hence induced emf $\varepsilon_1$ arises.
→When electric current $I _2$ flows through $C _2$, total magnetic flux linked with coil $C _1$ having $N _1$ turns is $N _1 \phi_1 \propto I _2$
$\therefore N _1 \phi_1= M I _2$
Where, M is mutual inductance
→For current changing with time,
$\frac{d}{d t}\left(N_1 \phi_1\right)= M \frac{d}{d t}\left( I _2\right)$
→According to Faraday's law, induced emf in $C _1$
$\varepsilon_1=-\frac{d}{d t}\left(N_1 \phi_1\right)$
→From equation (2) and (3),
$\varepsilon_1=- M \frac{d I _2}{d t}$
→Equation (4) is the required result.
→Here, value of induced emf depends on time rate of change of electric current and mutual inductance.
→In the figure, arrangement of two coil experiment is shown. Here, coils $C _1$ and $C _2$ are placed coaxially.
→When electric current $I _2$ passing through coil $C _2$ changes, magnetic flux linked with coil $C _1$ changes and hence induced emf $\varepsilon_1$ arises.
→When electric current $I _2$ flows through $C _2$, total magnetic flux linked with coil $C _1$ having $N _1$ turns is $N _1 \phi_1 \propto I _2$
$\therefore N _1 \phi_1= M I _2$
Where, M is mutual inductance
→For current changing with time,
$\frac{d}{d t}\left(N_1 \phi_1\right)= M \frac{d}{d t}\left( I _2\right)$
→According to Faraday's law, induced emf in $C _1$
$\varepsilon_1=-\frac{d}{d t}\left(N_1 \phi_1\right)$
→From equation (2) and (3),
$\varepsilon_1=- M \frac{d I _2}{d t}$
→Equation (4) is the required result.
→Here, value of induced emf depends on time rate of change of electric current and mutual inductance.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Define ionisation energy. How would the ionsation energy change when electron in hydrogen atom is replaced by a particle of mass 200 times that of the electron but having the same charge?
Two point charges $4\mu\text{C}$ and $-2 \mu\text{C}$ are separated by a distance of 1 m in air. Calculate at what point on the line joining the two charges is the electric potential zero.
→Discuss the intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids?
Describe/Explain single slit diffraction using a simple day to day life example.
###
Describe a simple experiment (/activity) to see single slit diffraction.
###
Describe a simple experiment (/activity) to see single slit diffraction.
Light possesses wave nature. It is strongly proved from which two experiments ?
A series LCR circuit with R = 20 Ω L = 1.5 H and $C=35 \mu F$ is connected to a variable frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?
→What are the readings of the ammeters A1 and A2 shown in figure. Neglect the resistance of the meters.
A double slit S1 - S2 is illuminated by a coherent light of wavelength $\lambda$. The slits are separated by a distance d. A plane mirror is placed in front of the double slit at a distance D1 from it and a screen $\sum$ is placed behind the double slit at a distance D2 from it (figure 17-E2). The screen E receives only the light reflected by the mirror. Find the fringe-width of the interference pattern on the screen.
→A copper wire bent in the shape of a semicircle of radius r translates in its plane with a constant velocity v. A uniform magnetic field B exists in the direction perpendicular to the plane of the wire. Find the emf induced between the ends of the wire if:
- The velocity is perpendicular to the diameter joining free ends.
- The velocity is parallel to this diameter.
Write (or mention) the achievements of Maxwell's Electro Magnetic wave theory and Hertz's experiment.