Advertisements
Advertisements
Question
Prove theoretically (electromagnetic induction) `e = (dphi)/(dt)`
Advertisements
Solution
1) Consider a rectangular loop of conducting wire ‘PQRS’ partly placed in uniform magnetic field of induction ‘B’ as shown in figure.
2) Let 'l' be the length of the side PS and 'x' be the length of the loop within the field.
∴ A = lx = area of the loop, which lies inside the field.
3) The magnetic flux (Φ) through the area A at certain time ‘t’ is Φ = BA = Blx
4) The loop is pulled out of the magnetic field of induction ‘B’ to the right with a uniform
velocity ‘v’.
5) The rate of change of magnetic flux is given by, `(dphi)/dt = d/dt (B/x)`
`:. (dphi)/dt = Bl (dx/dt)`
But, `((dx)/(dt)) = v`
`:. (dphi)/dt` = Blv ....(1)
6) Due to change in magnetic flux, induced current is set up in the coil. The direction of this current is clockwise according to Lenz’s law. Due to this, the sides of the coil experiences the forces, F1, F2 and F as shown in figure. The directions of these forces is given by Flemings left hand rule.
7) The magnitude of force ‘F’ acting on the side PS is given by, F = BIl.
8)The force `vecF_1` and `vecF_2` are equal in magnitude and opposite in direction, therefore they cancel out. The only unbalanced force which opposes the motion of the coil is `vecF` Hence, work must be done against this force in order to pull the coil.
9) The work done in time ‘dt’ during the small displacement ‘dx’ is given by, dW = - Fdx
- ve sign shows that F and ‘dx’ are opposite to each other.
∴dW = - (BIl) dx ….(2)
10) This external work provides the energy needed to maintain the induced current I
through the loop (coil).
11) If ‘e’ is the e.m.f induced then, electric power = `(dW)/dt = eI`
∴ dW = eIdt ....3
12) From equations (2) and (3),
eIdt = - BIl dx
:. `e = -Bl(dx/dt)`
∴ e = - Blv .....(4)
13) From equation (1) and (4), `e = - (dphi)/dt`
APPEARS IN
RELATED QUESTIONS
The magnetic flux through a loop varies according to the relation Φ = 8t2 + 6t + C, where ‘C’ is constant, 'Φ' is in milliweber and 't' is in second. What is the magnitude of induced e.m.f. in the loop at t = 2 seconds.
A solenoid of length 1.5 m and 4 cm in diameter possesses 10 turns per metre. A current of 5 A is flowing through it. The magnetic induction at a point inside the solenoid along the axis is ............................. .
(μ0 = 4π × 10-7 Wb/Am)
- π × 10-5 T
- 2π × 10-5 T
- 3π × 10-5 T
- 4π × 10-5 T
The device used for producing electric current is called _________.
State Fleming’s right-hand rule.
Explain different ways to induce current in a coil.
The phenomenon of electromagnetic induction is
Two circular coils A and B are placed closed to each other. If the current in the coil A is changed, will some current be induced in the coil B? Give reason.
A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s−1 in a direction normal to the
- longer side,
- shorter side of the loop?
For how long does the induced voltage last in each case?
If ‘R’ is the radius of dees and ‘B’ be the magnetic field of induction in which positive charges (q) of mass (m) escape from the cyclotron, then its maximum speed (vmax) is _______.
A) `(qR)/(Bm)`
B)`(qm)/(Br)`
C) `(qBR)/m`
D) `m/(qBR)`
How does an electromagnet differ forma permanent magnet?
Name two devices in which electromagnets are used and two devices where permanent magnets are used.
What is an electromagnet? Describe the construction and working of an electromagnet with the help of a labelled diagram.
The north-south polarities of an electromagnet can be found easily by using:
(a) Fleming's right-hand rule
(b) Fleming's left-hand rule
(c) Clock face rule
(d) Left-hand thumb rule
State whether the following statement are true or false:
A generator works on the principle of electromagnetic induction.
Name and state the law which determines the direction of induced current.
or
State Fleming’s right-hand rule.
Welders wear special goggles or face masks with glass windows to protect their eyes from electromagnetic radiations. Name the radiations and write the range of their frequency.
Show diagrammatically how an alternating emf is generated by a loop of wire rotating in a magnetic field. Write the expression for the instantaneous value of the emf induced in the rotating loop.
The coil of a moving-coil galvanometer keeps on oscillating for a long time if it is deflected and released. If the ends of the coil are connected together, the oscillation stops at once. Explain.
Consider the energy density in a solenoid at its centre and that near its ends. Which of the two is greater?
A conducting square loop of side l and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A uniform and constant magnetic field Bexists along the perpendicular to the plane of the loop as shown in figure. The current induced in the loop is _____________ .
L, C and R represent the physical quantities inductance, capacitance and resistance respectively. Which of the following combinations have dimensions of frequency?
(a) `1/(RC)`
(b) `R/L`
(c) `1/sqrt(LC)`
(d) C/L
Calculate the dimensions of (a) \[\int \overrightarrow{E} . d \overrightarrow{l,}\] (b) vBl and (c) \[\frac{d \Phi_B}{dt}.\] The symbols have their usual meaning.
A conducting square loop having edges of length 2.0 cm is rotated through 180° about a diagonal in 0.20 s. A magnetic field B exists in the region which is perpendicular to the loop in its initial position. If the average induced emf during the rotation is 20 mV, find the magnitude of the magnetic field.
Figure shows a long U-shaped wire of width l placed in a perpendicular magnetic field B. A wire of length l is slid on the U-shaped wire with a constant velocity v towards right. The resistance of all the wires is r per unit length. At t = 0, the sliding wire is close to the left edge of the U-shaped wire. (a) Calculate the force needed to keep the sliding wire moving with a constant velocity v. (b) If the force needed just after t = 0 is F0, find the time at which the force needed will be F0/2.0
The following diagram shows a fixed coil of several turns connected to a center zero galvanometer G and a magnet NS which can move in the direction shown in the diagram.
- Describe the observation in the galvanometer if
- The magnet is moved rapidly,
- The magnet is kept still after it has moved into the coil
- The magnet is then rapidly pulled out the coil.
- How would the observation in (i) of part (a) change if a more powerful magnet is used?
Fill in the blanks by writing (i) Only soft iron, (ii) Only steel, (iii) Both soft-iron and steel for the material of core and/or magnet.
D.C. motor ______.
Fill in the blanks by writing (i) Only soft iron, (ii) Only steel, (iii) Both soft-iron and steel for the material of core and/or magnet.
Transformer______.
Draw a labelled diagram to show how an electromagnet is made.
State the purpose of soft iron core used in making an electromagnet.
List some of the practical applications of an electromagnet.
The right-hand thumb rule is also called _______ rule.
Fleming's left hand rule : electric current : : Fleming's right hand rule : _______
A thin semi-circular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in the figure.
The potential difference developed across the ring when its speed v , is
State Fleming’s right-hand rule.
What for an inductor is used? Give some examples.
Establish the fact that the relative motion between the coil and the magnet induces an emf in the coil of a closed circuit.
Obtain an expression for motional emf from Lorentz force.
A square coil of side 30 cm with 500 turns is kept in a uniform magnetic field of 0.4 T. The plane of the coil is inclined at an angle of 30° to the field. Calculate the magnetic flux through the coil.
A straight metal wire crosses a magnetic field of flux 4 mWb in a time 0.4 s. Find the magnitude of the emf induced in the wire.
A coil of 200 turns carries a current of 4 A. If the magnetic flux through the coil is 6 x 10-5 Wb, find the magnetic energy stored in the medium surrounding the coil.
Metal rings P and Q are lying in the same plane, where current I is increasing steadily. The induced current in metal rings is shown correctly in figure.
A layer of atmosphere that reflects medium frequency radio waves which is ineffective during night, is ______.
A metal plate can be heated by ______.
The instrument that use to defect electric current in the circuit is known as ____________.
What should be the core of an electromagnet?
Ansari Sir was demonstrating an experiment in his class with the setup as shown in the figure below.
A magnet is attached to a spring. The magnet can go in and out of the stationary coil. He lifted the Magnet and released it to make it oscillate through the coil.
Based on your understanding of the phenomenon, answer the following question.
What will be observed when the Magnet starts oscillating through the coil. Explain the reason behind this observation.
Name some equipment that uses electromagnetism for functioning.
For making a strong electromagnet the material of the core should be ______.
Sea turtles return to their birth beach many decades after they were born due to ______.
A galvanometer is an instrument that can detect the presence of a current in a circuit.
A 0.4 m wire, stretched horizontally, carries an electric current of 15 A, in a magnetic field whose magnetic field intensity is 0.1 N/Am. What is the magnitude of the wire?
The working of a dynamo is based on the principle of
A rectangular, a square, a circular and an elliptical loop, all in the (x - y) plane, are moving out of a uniform magnetic field with a constant velocity `vecv = vhati`. The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for ______.
A current I = 10 sin(100π t) A is passed in first coil, which induces a maximum e.m.f of 5π volt in second coil. The mutual inductance between the coils is ______.
The primary of a transformer has 400 turns while the secondary has 2000 turns. If the power output from the secondary at 1000 Vis 12 kW, what is the primary voltage?
