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
JEE Main Pattern Exercise (1) 1. A straight wire of length m is carrying a current of 2A and the magnetic field due to it is measured at a point distant 1 cm from it. If the wire is to be bent into a circle and is to carry the same current as before, the ratio of the magnetic filed at its centre to that obtained in the first case would be(a) 1 : 100 (b) 100 : 1 (c) 1 : 50 (d) 50 : 1 2. An electron moving with a speed u along the positive x-axis at y = 0 centers a region of which exists to the right of y-axis. The electron exits from uniform magnetic field the region after sometime with speed ‘v’ at co-ordinate y, then-
(a) v>u, y0
(c) v>u, y>0 (d) v = u, y u, y < v = u, y > v > u, y > v = u, y <
sometime with speed ‘v’ at co-ordinate y, then0 0 0 0
2. An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the +x-direction and a magnetic field along the +z-direction, then (a) positive ions deflect towards +y-direction and negative ions towards –y-direction (b) all ions deflect towards +y-direction (c) all ions deflect towards –y-direction (d) positive ions deflect towards –y-direction and negative ions towards –y-direction
(Q 3) One or More Correct Options 3. An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true? (a) They will never come out of the magnetic field region (b) They will come out travelling along parallel paths (c) They will come out at the same time (d) They will come out at different times
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Electrodynamics (Q 4) Analytical Type Question 4. A proton and an alpha particle, after being accelerated through same potential difference, enter uniform magnetic field, the direction of which is perpendicular to their velocities. Find the ratio of radii of the circular paths of the two particles. 5. Two very long straight parallel wires carry steady currents I and –I respectively. The distance between the wires is d. At a certain instant of time, a point charge q is at a point equidistant from the two wires in the plane of the wires. Its instantaneous velocity v is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is (a) (b)
(c) (d) zero
6. A particle of mass m and charge q moves with a constant velocity v along the positive x-direction. It enters a region containing a uniform magnetic filed B directed along the negative z-direction, extending from x = a to x = b. The minimum value of v required so that the particle can just enter the region x > b is (a) (b)
(c) (d)
7. A proton, a deutron and an -particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rp, rd and rα denote, respectively the radii of the trajectories of these particles, then (a) rα = rp < rd (b) rα > rd > rp (c) rα = rd > rp (d) rp = rd = rα 8. H+, He+ and O2+ all having the same kinetic energy pass through a region in which there is a uniform magnetic field perpendicular to their velocity. The masses of H+, He+ and O2+ are 1 amu, 4 amu and 16 amu respectively. Then (a) H+ will be deflected most (b) O2+ will be deflected most (c) He+ and O2+ will be deflected equally (d) all will be deflected equally
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Electrodynamics (Q 9) Analytical Type Question 9. A beam of protons with a velocity × m/s enters a uniform magnetic field of 0.3 T at an angle of 60o to the magnetic field. Find : (i) The radius of the helical path taken by the proton beam. (ii) Find the pitch of the helix. (Q 10) Integer Answer Type Question 10. A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x, PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is , find the value of k.
ANSWER Q1
Q2
Q3
Q4
Q5
(d)
(c)
(b), (d)
(d)
Q6
Q7
Q8
Q9
(b)
(a)
(a), (c)
Q10 –2
(i) 1.2 × 10
m –2
(ii) 4.37 × 10
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m
I
