CLASS 12th
Electrodynamics
Electrodynamics
01. Magnetic Field Magnetic Field The magnetic field is a space around a conductor carrying current or the space around a magnet in which its magnetic effect can be felt. Moving charge is a source of both electric field as well as a magnetic field. Magnetic field is a vector. denoted by
, we deduce an expression for the force on a moving charge To define the magnetic field in a magnetic field. F ∝ q v sin θ B or F = k q v B sin θ Where k is a constant × × or Direction of Given by the Right-Handed-Screw rule or Right-Hand Rule.
02. Biot-Savart’s Law This law deals with the magnetic field induction at a point due to a small current element.
In SI Units,
sin dB = ×
In vector form, ×
Direction of d Right handed screw rule or Right Hand Rule. Biot Savart’s law in terms of charge (q) and its velocity (v) is.
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Electrodynamics × Important features of Biot Savart’s law (i) Biot Savart’s law is valid for a symmetrical current distribution. (ii) This law is analogous to Coulomb’s law in electrostatics. is perpendicular to both I and . (iii) The direction of d
03. Magnetic Field Due to a Straight Wire Carrying Current
sin dB = × cos or cos tan or tan sec cos cos cos sin sin
04. Magnetic Field at a Point on the Axis of a Circular Coil Carrying Current Plane of the coil be perpendicular to the plane of the paper and current I be flowing in there coil in the direction shown.
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Electrodynamics
sin (∵ a is small, therefore θ = 90°) dB = dB' = B =
Special cases (i)
(ii)
When point P lies at the centre of the circular coil, then x = 0, we have B = which is the same as given by above equation. When point P lies for away from the centre of the coil, then x >> a. Now a2 + x2 = x2 as a2 can be neglected in comparison to x2. From above equation, we have or
05. Ampere’s Circuital Law
around a Ampere’s circuital law states that the line integral of magnetic field induction closed path in vacuum is equal to μ0 times the total current I threading the closed path.
Application of Ampere’s Circuital Law is tangential to the loop or B is non-zero constant or (i) is normal to the loop or (ii)
vanishes. (iii)
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Electrodynamics
06. Magnetic Field Due to Infinite Long Straight Wire Carrying Current
It means the magnetic field due to current through infinite straight wire has a cylindrical symmetry.
07. Magnetic Field due to Current Through a Very Long Circular cylinder
or
or
cos
∝
08. The Solenoid A solenoid consists of an insulating long wire closely wound in the form of a helix. its length is very large as compared to its diameter.
over the closed path PQRS is The line integral of magnetic field induction
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Electrodynamics
(i) (ii)
BL = μ0 n LI A linear solenoid carrying current is equivalent to a bar magnet. The magnetic field lines due to current carrying solenoid resemble exactly with those of a bar magnet.
09. Toroid The toroid is hollow circular ring on which a large number of insulated turns of a metallic wire are closely wound. In fact, a toroid is an endless solenoid in the form of a ring.
cos
According to Ampere’s circuital law × total current or × or
10. Motion of A Charged Particle in a Uniform Electric Field , i.e., along OY. The direction of this force is in the direction of electric field
Acceleration along OY is,
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Electrodynamics
Using the relation This is an equation of parabola. Hence inside the electric field, the charged particle moves on a parabolic path OB and on leaving the field, it moves along a straight path BC, tangent to the curved path OB at B.
11. Motion of A Charged Particle in a Uniform Magnetic Field For component velocity , the force acting on the charged particle due to magnetic field is × or × sin sin
sin
12. Lorentz Force The force experienced by a charged particle moving in space where both electric and magnetic fields exist is called Lorentz force. Force due to electric field. Force due to magnetic field. × Due to both the electric and magnetic fields, ×
13. Cyclotron A cyclotron is a device developed by Lawrence and Livingstone by which the positively charged particles like proton, deutron, alpha particle etc. can be accelerated.
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Electrodynamics
Principle The working of the cyclotron is based on the fact that a positively charged particle can be accelerated to a sufficiently high energy with the help of smaller values of oscillating electric field by making it to cross the same electric field time and again with the use of strong magnetic field.
r =
This time is independent of both the speed of the ion and radius of the circular path.
14. Force on a Current Carrying Conductor Placed in a Magnetic Field Expression for the force acting on the conductor carrying current placed in a magnetic field.
Magnetic Lorentz Force × N = n (Al) = nAl ×
× sin
15. Force Between Two Parallel Linear Conductors Carrying Current Magnetic field induction at a point P on conductor C2 D2 due to current I1 passing through C1 D1 is given by
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Electrodynamics
Putting the value of B1, we have
16. Comparison of Electrical and Magnetic Forces
∈
×
17. Moving Coil Galvanometer Moving coil galvanometer is an instrument used for detection and measurement of small electric currents.
Its working is based on the fact that when a current carrying coil is placed in a uniform magnetic field it experiences a torque.
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Electrodynamics
Current sensitivity of a galvanometer is defined as the deflection produced in the galvanometer when a unit current flows thought it. Voltage sensitivity of a galvanometer is defined as the deflection produced in the galvanometer when a unit voltage is applied across the two terminals of the galvanometer. Condition for a sensitive galvanometer. A galvanometer is said to be very sensitive if it shows large deflection even when a small current is passed through it. From the theory of galvanometer.
18. Shunt Shunt is a low resistance connected in parallel with the galvanometer or ammeter. It protects the galvanometer or ammeter from the strong currents.
19. Ammeter An ammeter is a low resistance galvanometer. It is used to measure the current in a circuit in amperes.
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Electrodynamics
20. Voltmeter A voltmeter is a high resistance galvanometer. It is used to measure the potential difference between two points of a circuit in volt.
or or
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Electrodynamics
AIIMS Exercise (1) 1. In ‘Bohr’ model of atom, an electron is revolving in a circular orbit (n = 1) of radius R with frequency ω radian/sec. Find magnetic moment produced by the revolving electron. (a) (b)
(c) (d)
2. An infinitely long straight conductor is bent into the shape as shown in fig. It carries a current of I ampere and the radius of circular loop is r metre. Find the magnetic induction at the centre of the circular part.
(a) , inwards (b) , inwards (c) , inwards (d) , inwards 3. A coil having 21 turns is would tightly in the form of a spiral with inner radius 2 cm and outer radius 4 cm. If a current of 10 amp flows through it its magnetic moment is : (a) 0516 Am2 (b) 0.25 Am2
(c) 0.616 Am2 (d) 0.414 Am2
4. A ring of radius R, made of an insulating material carries a charge q uniformly distributed on it. If the ring rotates about the axis passing through its centre and normal to plane of the ring with constant angular speed ω, then the magnitude of the magnetic moment of the ring is : (a) (b)
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(c) (d)
Electrodynamics 5. A helium nucleus makes full rotation in a circle of radius 0.8 m in 2 seconds. The value of magnetic field B at the centre of the circle will be (μ0 = permeability constant) : (a) (b) 2 × 10‒19 μ0 (c) 10‒19 μ0 × (d) 6. A vertical wire carries a current of 20 A. If the neutral point is observed at a distance of 2.0 m from the wire, calculate the horizontal component of earth’s magnetic field. (a) 2.0 × 10‒5 T (b) 2.0 × 10‒4 T (c) 3.17 × 10‒4 T (d) 0.3 × 10‒2 T 7. A uniform wire of length l is first turned into two turns. The same wire is then bent into the three turns. If the same current is passed in both the cases, calculate the ratio of magnetic field
in the two cases :
(a) (b)
(c) (d)
8. A deuteron of kinetic energy 50 keV is describing a circular orbit of radius 0.5 m in a plane perpendicular to magnetic field B. The kinetic energy of the proton that describes a circular orbit of radius 0.5 m in the same plane with the same B is : (a) 25 keV (b) 50 keV
(c) 200 keV (d) 100 keV
9. A long solenoid is formed by closely winding the insulated wire so that the successive turns touch each other. The radius of the wire is 0.5 mm. If a current of 10 A is passed through it, find the magnetic field induction at one end of the solenoid. (a) π × 10‒3 T (b) 2 × 10‒3 T (c) 2π × 10‒3 T (d) 4π × 10‒3 T
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Electrodynamics 10. A solenoid is 2m long and 2 cm in mean diameter. It has five layers of windings of 200 turns each and carries a current of 10 A. What is the magnetic field at its centre? (a) 6.28 × 10‒2 T (b) 3.14 × 10‒3 T (c) 6.28 × 10‒3 T (d) None of these 11. The magnetic flux through a coreless solenoid carrying current i is 5 × 10‒6 Wb. If the length of solenoid is 25 cm, its magnetic moment is equal to : (a) 1 Am2 (b) 10 Am2
(c) 12.5 Am2 (d) 125 Am2
12. Two electrons move parallel to each other with equal velocities 6 × 105 ms‒1 each. Find the ratio of electric and magnetic interaction forces between them. (a) 3 × 108 (b) 9 × 1016
(c) 2.5 × 105 (d) 9 × 105
In each of the following questions, a statement of Assertion (A) is followed by a corresponding statement of Reason (R). Of the following statements, choose the correct one. (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not correct explanation of A. (c) A is true but R is false. (d) A is false but R is true. (e) Both A and R are false. 13. (A) : An electron with larger velocity of throw in an electric field will experience a larger force. (R) : An electron projected perpendicular to magnetic field follows a circular path. 14. (A) : Two rods connected in parallel to a battery, attract each other. (R) : Parallel wires carrying currents in the same direction repel each other.
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Electrodynamics
AIIMS Exercise (2) 1. Two long straight conducting wires A and B are separated by a distance of 12 cm and are fixed rigidly and carry currents of 2 A and 6 A respectively in the same direction. Where should a third wire C carrying current of 5 A in the same direction be placed so that it remains in equilibrium? (a) 2 cm from A (b) 4 cm from A (c) 6 cm from A (d) 3 cm from A
2. A long straight wire AB carries a current of 4A. A proton P travels with a speed 4 × 106 ms‒1, parallel to the wire, at 0.2 m distance from it and in a direction opposite to the current as shown in fig. Calculate the force exerted on the proton by the magnetic field of current.
(a) (b) (c) (d)
2.0 × 109 N away from AB 2.56 × 10‒18 N away from AB 1.28 × 10‒9 N away from AB 12.0 × 10‒18 N away from AB
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Electrodynamics 3. A charged particle of mass m and charge q is projected in a uniform magnetic field of width ‘a’ acting perpendicular to its velocity. Find the angle of deviation α of the particle as it comes out of the magnetic field.
(a) cos (b) sin
(c) tan (d) sin
4. A coil of area 0.2 m2 has 200 turns. It is kept with its plane inclined at an angle of 60°, from a uniform magnetic field induction of strength 2 × 10‒4 tesla. Calculate the torque acting on the coil, if it carries a current of 10 amp. (a) 2 × 10‒2 N-m (b) 3 × 10‒2 N-m (c) 4 × 10‒2 N-m (d) 16 × 10‒2 N-m 5. A wire carrying a current of 5A is bent in the form of a parabola y2 = 9‒x as shown in fig. tesla. The where x and y are in metre. The wire is placed in a uniform magnetic field B = 2 force acting on the wire is :
(a) 60 N (b) 90 N
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(c) 30 N (d) zero
Electrodynamics 6. A wire of length l can be formed into many circular loops of varying radii r depending on the number of turns n. The loop so formed is carrying a current and placed perpendicular to a uniform magnetic field. For torque to be maximum in the field, the number of turns n must be : (a) 1 (b) 4
(c) 8 (d) ∞
7. A cyclotron is accelerating proton. The applied magnetic field is 2 T and the potential difference in the gap is 100 kV. For how many turns has the proton to move between the dees to acquire a kinetic energy of 20 MeV? (a) 200 (b) 300
(c) 150 (d) 100
8. Deuterons in a cyclotron revolve in a circle of radius 50 cm just before emerging from the D’s. The frequency of applied alternating voltage is 7 MHz. Find the speed of the deuterons upon emergency : (a) 1.1 × 107 ms‒1 (b) 2.2 × 107 ms‒1 (c) 3.3 × 107 ms‒1 (d) 4.4 × 106 ms‒1 9. A 2 MeV proton is moving perpendicular to a uniform magnetic field 2.5 T. Force on the proton is : (a) 2.5 × 10‒10 N (b) 8 × 10‒11 N (c) 2.5 × 10‒11 N (d) 8 × 10‒12 N 10. A fixed horizontal wire carries a current of 200 A. another wire having mass per unit length 10‒2 kg/m is placed below the first at a distance of 2 cm and parallel to it. How much current be passed through the second wire so that it floats in air without any support? (a) 4.9 A (b) 49 A
(c) 9.8 A (d) 24.5 A
11. The maximum energy of a deuteron coming out of a cyclotron accelerator is 10 MeV. The maximum energy of protons that can be obtained form this accelerator is : (a) 10 MeV (b) 30 MeV
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(c) 40 MeV (d) 20 MeV
Electrodynamics 12. A moving coil galvanometer gives a deflection of 5° when a current of 2 amp flows through it. If the number of turns is increased to two times and the suspension wire is replaced by a wire of one third stiffness then the deflection in galvanometer with 4 amp current is : (a) 10° (b) 30°
(c) 40° (d) 60°
In each of the following questions, a statement of Assertion (A) is followed by a corresponding statement of Reason (R). Of the following statements, choose the correct one. (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not correct explanation of A. (c) A is true but R is false. (d) A is false but R is true. (e) Both A and R are false. 13. (A) : Magnetic flux is a vector quantity. (R) : Value of magnetic flux can be positive, negative or zero. 14. (A) : When a charged particle is projected with some velocity in a uniform magnetic field, its K.E. never increases. × (R) :
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