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 metal rod `1/sqrtpi `m long rotates about one of its ends perpendicular to a plane whose magnetic induction is 4 x 10-3 T. Calculate the number of revolutions made by the rod per second if the e.m.f. induced between the ends of the rod is 16 mV.
When a bar magnet is pushed towards (or away) from the coil connected to a galvanometer, the pointer in the galvanometer deflects. Identify the phenomenon causing this deflection and write the factors on which the amount and direction of the deflection depends. State the laws describing this phenomenon.
It is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of area 2 cm2 with 25 closely wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region. Equivalently, one can give it a quick 90° turn to bring its plane parallel to the field direction. The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5 mC. The combined resistance of the coil and the galvanometer is 0.50 Ω. Estimate the field strength of magnet.
The magnetic flux through a loop is varying according to a relation `phi = 6t^2 + 7t + 1` where `phi` is in milliweber and t is in second. What is the e.m.f. induced in the loop at t = 2 second?
A circular coil of cross-sectional area 200 cm2 and 20 turns is rotated about the vertical diameter with angular speed of 50 rad s−1 in a uniform magnetic field of magnitude 3.0 × 10−2T. Calculate the maximum value of the current in the coil.
Name a common device that uses electromagnets.
What is an electromagnet? Describe the construction and working of an electromagnet with the help of a labelled diagram.
Write some of the important uses of electromagnets.
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
When a wire is moved up and down in a magnetic field, a current is induced in the wire. What is this phenomenon known as?
Name one device which works on the phenomenon of electromagnetic induction.
Describe different ways to induce current in a coil of wire.
When the magnet shown in the diagram below is moving towards the coil, the galvanometer gives a reading to the right.
() What is the name of the effect being produced by the moving magnet?
(2) State what happens to the reading shown on the galvanometer when the magnet is moving away from the coil.
(3) The original experiment is repeated. This time the magnet is moved towards the coil at a great speed. State two changes you would notice in the reading on the galvanometer.
Describe one experiment to demonstrate the phenomenon of electromagnetic induction.
- What kind of energy change takes place when a magnet is moved towards a coil having a galvanometer at its ends?
- Name the phenomenon.
A light metal disc on the top of an electromagnet is thrown up as the current is switched on. Why? Give reason.
Electromagnetic induction means ______.
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 _____________ .
The switches in figure (a) and (b) are closed at t = 0 and reopened after a long time at t = t0.
(a) The charge on C just after t = 0 is εC.
(b) The charge on C long after t = 0 is εC.
(c) The current in L just before t = t0 is ε/R.
(d) The current in L long after t = t0 is ε/R.
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
Draw a simple labeled diagram of a step-up transformer.
The diagram 10 shows two coils X and Y. The coil X is connected to a battery S and a key K. The coil Y is connected to a galvanometer G.
When the key K is closed. State the polarity
(i)At the end of the coil X,
(ii)At the end C of the coil Y,
(iii)At the end C of the coil Y if the coil Y is (a) Moved towards the coil X, (b) Moved away from the coil X.
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.
A. C. generator______.
Name the following diagram and explain the concept behind it.
State Fleming’s Right Hand Rule.
Answer the following:
State the principles of the electric motor and electric generator.
State the purpose of soft iron core used in making an electromagnet.
List two ways of increasing the strength of an electromagnet if the material of the electromagnet is fixed.
What is an electromagnet? What do you know about the simplest form of an electromagnet?
Draw a labelled diagram to make an electromagnet from a soft iron bar. Mark the polarity at its ends in your diagram. What precaution would you observe while making it?
State the condition at which we say the two coils kept close to each other are perfectly coupled with each other.
Observe the given figure of Fleming’s Right Hand Rule and write the labels of A and B correctly.
Find the odd one out and give its explanation.
Write the two names in the following diagram.
Right hand thumb 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.
Obtain an expression for motional emf from Lorentz force.
A 50 cm long solenoid has 400 turns per cm. The diameter of the solenoid is 0.04 m. Find the magnetic flux linked with each turn when it carries a current of 1 A.
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 ______.
A metal plate can be heated by ______.
The condition for the praenomen of electromagnetic induction is that there must be a relative motion between ____________.
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.
Which of the following instruments works by electromagnetic induction?
Sea turtles return to their birth beach many decades after they were born due to ______.
One solenoid is centered inside another. The outer one has a length of 50.0 cm and contains 6750 coils, while the coaxial inner solenoid is 3.0 cm long and π cm2 in area and contains 150 coils. The current in the outer solenoid is changing at 3000 A/s. The emf induced in the inner solenoid is ______ V.
(Round off to two decimal places.)
