Advertisements
Advertisements
Question
Using Ampere's law, obtain an expression for the magnetic induction near a current-carrying straight infinitely long wire.
Advertisements
Solution
- Consider a long straight wire carrying a current I as shown in the figure below.
A long straight current-carrying wire
`vec"B"` and `vec"d""l"` are tangential to the Amperian loop which in this case is a circle.
∴ `vec"B"` . `vec"d""l" = "B dl"`
= B r dθ - The field `vec"B"` at a distance r from the wire is given by
B = `mu_0/(2pi) "I"/"r"`
∴ `oint_"c" vec"B".vec"d""l" = int_0^(2pi) (mu_0 "I")/(2pi "r") "r d" theta = mu_0 "I"`
APPEARS IN
RELATED QUESTIONS
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 _________.
The phenomenon of electromagnetic induction is
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?
What is electromagnetic induction?
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)`
State three ways in which the strength of an electromagnet can be increased.
What is an electromagnet? Describe the construction and working of an electromagnet with the help of a labelled diagram.
Explain why, the core of an electromagnet should be of soft iron and not of steel.
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
An induced current is produced when a magnet is moved into a coil. The magnitude of induced current does not depend on:
(a) the speed with which the magnet is moved
(b) the number of turns of the coil
(c) the resistivity of the wire of the coil
(d) the strength of the magnet
How is the working of an electric bell affected, if alternating current be used instead of direct current?
In which of the following case does the electromagnetic induction occur?
The current is stopped in a wire held near a loop of wire .
In which of the following case does the electromagnetic induction occur?
A magnet is moved through a loop of wire .
Electromagnetic induction means ______.
A conducting rod is moved with a constant velocity v in a magnetic field. A potential difference appears across the two ends _____________ .
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.
Draw and label the diagram of a simple D.C. motor.
(a) Explain the rotation of the coil, giving a reason for your answer.
(b) How can you reverse the direction of rotation of the armature?
(c) How can you increase the speed of rotation of the motor?
Fig. shows a simple form of an A.C. generator.
(a) Name the parts labeled A and B.
(b) What would be the effect of doubling the number of turns on the coil if the speed of rotation remains unchanged?
(c) Which of the output terminals is positive if the coil is rotating in the
direction shown in the diagram (anticlockwise)?
( d ) What is the position of the rotating coil when p.d. across its ends is zero? Explain why p.d. is zero when the coil is at this position .
(e) Sketch a graph showing how the p.d. across the ends of the rotating coil varies with time for an A.C. dynamo.
( f) On th e same sheet of paper and vertically below the first graph using the same time scale, sketch graphs to show the effect of
(i) Doubling the speed of rotation and at the same time keeping
the field and the number of turns constant,
(ii ) Doubling the number of turns on the coil and at the same time
doubling the speed of rotation of the coil, keeping th e speed
constant.
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______.
State Fleming’s Right Hand Rule.
Answer the following:
State the principles of the electric motor and electric generator.
Draw a labelled diagram to show how an electromagnet is made.
State the purpose of soft iron core used in making an electromagnet.
What is an electromagnet? What do you know about the simplest form of an electromagnet?
The diagram shows a rectangular coil ABCD, suspended freely between the concave pole pieces of a permanent horseshoe magnet, such that the plane of the coil is parallel to the magnetic field.
- State your observation when the current is switched on.
- Give an explanation for your observation in (i).
- State the rule, which will help you to find the motion of rotation of the coil.
- In which position will the coil ultimately come to rest?
- State four ways of increasing the magnitude of force acting on the coil.
The energy stored in a 50 mH inductor carrying a current of 4 A is ______
Fleming's left hand rule : electric current : : Fleming's right hand rule : _______
An electron moves on a straight-line path XY as shown in the figure. The coil abcd is adjacent to the path of the electron. What will be the direction of the current, if any, induced in the coil?
State Lenz’s law.
Show that Lenz’s law is in accordance with the law of conservation of energy.
The magnetic flux passing through a coil perpendicular to its plane is a function of time and is given by OB = (2t3 + 4t2 + 8t + 8) Wb. If the resistance of the coil is 5 Ω, determine the induced current through the coil at a time t = 3 second.
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.
Using Lenz’s law, predict the direction of induced current in conducting rings 1 and 2 when the current in the wire is steadily decreasing.
A layer of atmosphere that reflects medium frequency radio waves which is ineffective during night, is ______.
There is a uniform magnetic field directed perpendicular and into the plane of the paper. An irregular shaped conducting loop is slowly changing into a circular loop in the plane of the paper. Then ______.
The instrument that use to defect electric current in the circuit is known as ____________.
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 is the principle which Ansari Sir is trying to demonstrate?
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.
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.
Consider the situation where the Magnet goes in and out of the coil. State two changes which could be made to increase the deflection in the galvanometer.
Name some equipment that uses electromagnetism for functioning.
For making a strong electromagnet the material of the core should be ______.
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?
AB is a coil of copper wire having a large number of turns. The ends of the coil are connected with a galvanometer as shown. When the north pole of a strong bar magnet is moved towards end B of the coil, a deflection is observed in the galvanometer.
- State the reason for using galvanometer in the activity and why does its needle deflects momentarily when magnet is moved towards the coil.
- What would be observed in the galvanometer in a situation when the coil and the bar magnet both move with the same speed in the same direction? Justify your answer.
- State the conclusion that can be drawn from this activity.
Will there be any change in the momentary deflection in the galvanometer if number of turns in the coil is increased and a more stronger magnet is moved towards the coil?
OR
What is electromagnetic induction? What is observed in the galvanometer when a strong bar magnet is held stationary near one end of a coil of large number of turns? Justify your answer.
A conducting bar of length L is free to slide on two parallel conducting rails as shown in the figure
Two resistors R1 and R2 are connected across the ends of the rails. There is a uniform magnetic field `vec"B"` pointing into the page. An external agent pulls the bar to the left at a constant speed v. The correct statement about the directions of induced currents I1 and I2 flowing through R1 and R2 respectively is:
In the given circuit, initially switch S1 is closed and S2 and S3 are open. After charging of capacitor, at t = 0, S1 is open and S2 and S3 are closed. If the relation between inductance capacitance and resistance is L = 4CR2 then the time (in sec) after which current passing through capacitor and inductor will be same is ______ × 10-4 N. (Given R = ℓn(2)mΩ, L = 2mH)
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 ______.
An expression for oscillating electric field in a plane electromagnetic wave is given as Ez = 300 sin(5π × 103x - 3π × 1011t)Vm-1 Then, the value of magnetic field amplitude will be ______. (Given: speed of light in Vacuum c = 3 × 108 ms-1)
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?
