PART - 2
This session makes a great deal of formulae , connecting thread of ( PART - 1 ) . This part consist of laws of electric and magnetic field. If you want to be a rock and Roll star follow ME..:)
1 - Kirchhoff"s law → ΣI = 0 ( it follows from conservation of charge.) [ LOOP RULE]
Σε = ΣRI ( it follows from law of conservation of energy ) [ JUNCTIONS LAW ]
2 - Wheatstone bridge → P/Q = R/S ( is the condition for a balanced Wheatstone bridge .)
3 - Principal of a potentiometer → V ∝ l ( that is fall of potential across a wire is directly proportional to the length of the wire.)
4 - Comparison of emf of two cells →Ɛ₁ / Ɛ₂ = l₁/ l₂ ( Ɛ₁ and Ɛ₂ are the emfs of two cells and l₁ and l₂ are the corresponding balancing lengths of the potentiometer wire .)
5 - Internal resistance of a cell → r = [ (l₁ - l₂ ) / l₂ ] R ( l₁ and l₂ are the balancing lengths without and with a resistance R connected to the cell.)
6 - Electric energy → VIt ( V is the potential difference and t is the for which current I flows .)
7 - Heat →H = VIt/4.2 = I²Rt/4.2 ( Heat produced in calorie , when a current I flows through a resistor of resistance R.)
8 - Electric power → Pʀ = VI = I²R = V²/ R ( Pʀ is the power dissipated in a resistor of resistance R when a potential difference V applied across its ends and as a result , a current I flows through it .)
9 - Power output of a source → Ps → ƐI ( Ps is power output of a source of emf Ɛ and I is the current delivered by it .)
10 - Lorentz force → Fₘ = q ( v ⨯B ) ( where v and B is in vector form.)
Fₘ = qvB sinθ ( Fₘ is the magnetic Lorentz force acting on a charged particle of charge q and moving with a velocity v in a magnetic field B . θ is the angle between v and B.)
11 - Cyclotron radius → r = mv/qB ( r is the radius of the circular path which a charged particle having mass m follows when moving with a velocity v initially at right angle to the magnetic field B . This radius is called Gyroradius or cyclotron radius.)
12 - Cyclotron frequency → v = qB / 2 𝝅m
13 - Kinetic energy → K = q²B²R² / 2m ( K is the maximum kinetic energy of the charged particle of charge q and mass m emerging out of a cyclotron with dee radius R , B is the magnetic field perpendicular to the plane of the dees.)
14 - Force acting on a straight conductor → F = IlB ( F is a force acting on a straight conductor of length l and carrying a current I when placed in a uniform external magnetic field B . l is the direction of current .)
15 - Torque → ꞇ = NIABsin θ ( ꞇ Acting on a coil of N turns of Area A and carrying a current I is when placed in a uniform magnetic field B here A is perpendicular to the plane of the coil and θ is the angle between A and B .)
ꞇ = NIABcosα ( α is the angle between B and the plane of the coil.)
16 - Torque → ꞇ = m x B ( ꞇ is the torque acting on a current loop placed in a magnetic field B and m is the magnetic dipole moment of the current loop that is current carrying loop m = NIA.)
17 - Current sensitivity → CS = θ/ I = NAB/k
Voltage sensitivity of a galvanometer → VS = θ/V = NAB / kR = CS / R ( k is called the torsional constant and R is the resistance of the galvanometer .)
18 - Shunt resistance → S = Iℊ G/ ( I - Iℊ) = G / ( n - 1) ( S is the shunt resistance require to convert a galvanometer of resistance G into a ammeter to measure a current I . Iℊ is the current that can safely flow through the galvanometer without damaging it or current which produces full scale deflection in the galvanometer .Iℊ also stands for the given current range and I is the required current range.)
19 - Biot - Savart Law → B = kₘ ( Il x r )/ r³ ( B is the magnetic field at any point due to a current element l carrying a current I . r is the vector from the current element to the point. kₘ is the magnetic constant. )
20 - Magnetic field → B = kₘ (2l/a) = μ₀ I/2πa ( B is the magnetic field due to an infinitely long conductor at a point distance 'a' from it .)
B = kₘ (I/a) = μ₀I/ 4πa ( When the point lies at a distance 'a' near one end of an infinitely long conductor .)
21 - Force per unit length between two straight parallel infinite conductor → f = kₘ (2 I₁I₂ ) / a = (μ₀I₁I₂)/ 2πa ( The force is attractive if the currents are in the same direction and repulsive if they are in opposite directions.)
22 - Magnetic field at the center of a coil → B = kₘ (2πNI)/r = (μ₀NI)/2r (Magnetic field at the center of a coil of radius r and N turns through which I current flows .)
23 - Magnetic field due to a coil at a point on its axis → B = kₘ (2πNI∮R² )/ (R² + x²)³/²
= (μ₀NIR²)/ 2(R² + x²)³/² ( B is the magnetic field due to a coil N turns radius R and through which a current I flows at a point on its axis distance x from the center .)
24 - Magnetic field inside a long solenoid → B = μ₀ nI ( B is the magnetic field inside a long solenoid carrying a current I at points near its center and n is the number of turns per unit length .)
B = (μ₀nI)/2 ( B is the magnetic field at a point situated at one of the ends of a long solenoid.)
25 - Magnetic field inside a tortoid → B = (μ₀NI )/ 2πr ( B is the magnetic field inside a tortoid of a radius r having N turns .)
26 - Ampere's Circuital Law → ∮ B.dl = μ₀ I ( The line integral in the equation is evaluated around a closed loop called an Amperean loop and I is the net current encircled by the loop.)
27 - Magnetic Flux → ɸʙ = BS (ɸʙ is the magnetic flux linked with a surface of area S placed perpendicular to a uniform magnetic field B)
28 - Gauss's law of magnetism → ∮B.dS = 0
29 - Magnetic dipole moment → m = qₘ x 2a = 2qₘa ( m is the magnetic dipole moment of a magnetic dipole whose each pole has a strength qₘ.)
30 - Magnetic field due to a dipole on its axial line → Bₐₓᵢₐₗ→ kₘ (2mr)/ (r² - a²)²
For a short dipole → Bₐₓᵢₐₗ = kₘ 2m/r³ ( Bₐₓᵢₐₗ is the magnetic field due to a dipole on its axial line , at a point distance r from its center.)
31 - Magnetic field due to a dipole on its equatorial line → Bₑ𝔮ᵤₐₜₒᵣᵢₐₗ → kₘ = m/(r² + a² )³/²
Bₑ𝔮ᵤₐₜₒᵣᵢₐₗ = kₘ m/r³ ( for a short dipole )
32 - Magnetic potential energy → Uʙ = - m . B = - mBcosθ ( Uʙ is the magnetic potential energy of the dipole in an external uniform field B making an angle θ with B .)
33 - Time period → T = 2π✓I /mB ( T is the time period of a freely suspended magnet of magnetic moment m and moment of inertia I in a magnetic field B .)
34 - Horizontal component → Bʜ = B cos 𝛿, Bv =Bsin𝛿 and B = ✓B²ʜ + B²v ( B is the resultant magnetic field at a place on earth with dip 𝛿 and Bʜ , Bv are the horizontal and the vertical components of B .)
35 - Magnetic susceptibility → 𝒳ₘ = M/H ( 𝒳ₘ is called the magnetic susceptibility , which is a dimensionless quantity and has no units .)
36 - Induced emf → ε = - dФʙ / dt ( ε is the induced emf set up in a circuit when the rate of change of flux is dФʙ / dt .)
37 - Induced emf set up across the ends of a conductor → ε = Blv ( ε is the induced emf set up across the ends of a conductor of length l when moving in a magnetic field B with a velocity v and in a direction perpendicular to B.)
38 - Faraday's law in general form → ε = ∮ E .dl ( E is a non conservative , time varying electric field that is produced by the changing magnetic flux .)
The essence of the law is that a changing magnetic flux induces an electric field.
ε = 1/2 B⍵l² ( ε is the emf induced in a rod of length l rotating with constant angular speed ⍵ in a uniform magnetic field .)
ε = NAB⍵sinθ ( ε is the induced emf in the rotating armature of a dynamo whose total number of turns is N ,area is A , B is the magnetic induction ,⍵ is the angular velocity and θ is the angle between B and A .)
39 - Current → I = (V - ε ) /R ( I is the current through the armature coil of a dc motor of resistance R . Here V is the applied voltage and ε is the back emf .)
40 - Efficiency of dc motor → 𝜼 = ε / V
41 - Self induction → L = Φʙ / I ( L is the self induction of the coil and Фʙ is the magnetic flux linked with it when a current I flows through it.)
42 - Coefficient of self induction → ε = L ( dl/dt) ( ε is the induced emf set up in a coil when the rate of change of current in the coil is dl/dt . L is the coefficient of self induction or self inductance or simply the inductance of coil . Inductance is the measure of the opposition of a device to a change in current.)
43 - Inductance of a solenoid → L = (μ₀N²A / l ) ( L is the inductance of a solenoid whose core is a vacuum ), N is the total number of turns , A is the cross sectional area and l is the length of a solenoid .)
44 - Mutual induction → Фʙ = MI ( M is the mutual induction of two coils , I being the current through one coil and Фʙ is the flux linked with the other coil.)
45 - Energy stored in the magnetic field of an inductor → Uʙ = 1/2 LI²
46 - Magnetic energy density → uʙ = B²/ 2μ₀ ( uʙ is the magnetic energy density at a point where the magnetic field is B . Thus the energy density is proportional to the square of the field at that point. )
5 - Internal resistance of a cell → r = [ (l₁ - l₂ ) / l₂ ] R ( l₁ and l₂ are the balancing lengths without and with a resistance R connected to the cell.)
6 - Electric energy → VIt ( V is the potential difference and t is the for which current I flows .)
7 - Heat →H = VIt/4.2 = I²Rt/4.2 ( Heat produced in calorie , when a current I flows through a resistor of resistance R.)
8 - Electric power → Pʀ = VI = I²R = V²/ R ( Pʀ is the power dissipated in a resistor of resistance R when a potential difference V applied across its ends and as a result , a current I flows through it .)
9 - Power output of a source → Ps → ƐI ( Ps is power output of a source of emf Ɛ and I is the current delivered by it .)
10 - Lorentz force → Fₘ = q ( v ⨯B ) ( where v and B is in vector form.)
Fₘ = qvB sinθ ( Fₘ is the magnetic Lorentz force acting on a charged particle of charge q and moving with a velocity v in a magnetic field B . θ is the angle between v and B.)
11 - Cyclotron radius → r = mv/qB ( r is the radius of the circular path which a charged particle having mass m follows when moving with a velocity v initially at right angle to the magnetic field B . This radius is called Gyroradius or cyclotron radius.)
12 - Cyclotron frequency → v = qB / 2 𝝅m
13 - Kinetic energy → K = q²B²R² / 2m ( K is the maximum kinetic energy of the charged particle of charge q and mass m emerging out of a cyclotron with dee radius R , B is the magnetic field perpendicular to the plane of the dees.)
14 - Force acting on a straight conductor → F = IlB ( F is a force acting on a straight conductor of length l and carrying a current I when placed in a uniform external magnetic field B . l is the direction of current .)
15 - Torque → ꞇ = NIABsin θ ( ꞇ Acting on a coil of N turns of Area A and carrying a current I is when placed in a uniform magnetic field B here A is perpendicular to the plane of the coil and θ is the angle between A and B .)
ꞇ = NIABcosα ( α is the angle between B and the plane of the coil.)
16 - Torque → ꞇ = m x B ( ꞇ is the torque acting on a current loop placed in a magnetic field B and m is the magnetic dipole moment of the current loop that is current carrying loop m = NIA.)
17 - Current sensitivity → CS = θ/ I = NAB/k
Voltage sensitivity of a galvanometer → VS = θ/V = NAB / kR = CS / R ( k is called the torsional constant and R is the resistance of the galvanometer .)
18 - Shunt resistance → S = Iℊ G/ ( I - Iℊ) = G / ( n - 1) ( S is the shunt resistance require to convert a galvanometer of resistance G into a ammeter to measure a current I . Iℊ is the current that can safely flow through the galvanometer without damaging it or current which produces full scale deflection in the galvanometer .Iℊ also stands for the given current range and I is the required current range.)
19 - Biot - Savart Law → B = kₘ ( Il x r )/ r³ ( B is the magnetic field at any point due to a current element l carrying a current I . r is the vector from the current element to the point. kₘ is the magnetic constant. )
20 - Magnetic field → B = kₘ (2l/a) = μ₀ I/2πa ( B is the magnetic field due to an infinitely long conductor at a point distance 'a' from it .)
B = kₘ (I/a) = μ₀I/ 4πa ( When the point lies at a distance 'a' near one end of an infinitely long conductor .)
21 - Force per unit length between two straight parallel infinite conductor → f = kₘ (2 I₁I₂ ) / a = (μ₀I₁I₂)/ 2πa ( The force is attractive if the currents are in the same direction and repulsive if they are in opposite directions.)
22 - Magnetic field at the center of a coil → B = kₘ (2πNI)/r = (μ₀NI)/2r (Magnetic field at the center of a coil of radius r and N turns through which I current flows .)
23 - Magnetic field due to a coil at a point on its axis → B = kₘ (2πNI∮R² )/ (R² + x²)³/²
= (μ₀NIR²)/ 2(R² + x²)³/² ( B is the magnetic field due to a coil N turns radius R and through which a current I flows at a point on its axis distance x from the center .)
24 - Magnetic field inside a long solenoid → B = μ₀ nI ( B is the magnetic field inside a long solenoid carrying a current I at points near its center and n is the number of turns per unit length .)
B = (μ₀nI)/2 ( B is the magnetic field at a point situated at one of the ends of a long solenoid.)
25 - Magnetic field inside a tortoid → B = (μ₀NI )/ 2πr ( B is the magnetic field inside a tortoid of a radius r having N turns .)
26 - Ampere's Circuital Law → ∮ B.dl = μ₀ I ( The line integral in the equation is evaluated around a closed loop called an Amperean loop and I is the net current encircled by the loop.)
27 - Magnetic Flux → ɸʙ = BS (ɸʙ is the magnetic flux linked with a surface of area S placed perpendicular to a uniform magnetic field B)
28 - Gauss's law of magnetism → ∮B.dS = 0
29 - Magnetic dipole moment → m = qₘ x 2a = 2qₘa ( m is the magnetic dipole moment of a magnetic dipole whose each pole has a strength qₘ.)
30 - Magnetic field due to a dipole on its axial line → Bₐₓᵢₐₗ→ kₘ (2mr)/ (r² - a²)²
For a short dipole → Bₐₓᵢₐₗ = kₘ 2m/r³ ( Bₐₓᵢₐₗ is the magnetic field due to a dipole on its axial line , at a point distance r from its center.)
31 - Magnetic field due to a dipole on its equatorial line → Bₑ𝔮ᵤₐₜₒᵣᵢₐₗ → kₘ = m/(r² + a² )³/²
Bₑ𝔮ᵤₐₜₒᵣᵢₐₗ = kₘ m/r³ ( for a short dipole )
32 - Magnetic potential energy → Uʙ = - m . B = - mBcosθ ( Uʙ is the magnetic potential energy of the dipole in an external uniform field B making an angle θ with B .)
33 - Time period → T = 2π✓I /mB ( T is the time period of a freely suspended magnet of magnetic moment m and moment of inertia I in a magnetic field B .)
34 - Horizontal component → Bʜ = B cos 𝛿, Bv =Bsin𝛿 and B = ✓B²ʜ + B²v ( B is the resultant magnetic field at a place on earth with dip 𝛿 and Bʜ , Bv are the horizontal and the vertical components of B .)
35 - Magnetic susceptibility → 𝒳ₘ = M/H ( 𝒳ₘ is called the magnetic susceptibility , which is a dimensionless quantity and has no units .)
36 - Induced emf → ε = - dФʙ / dt ( ε is the induced emf set up in a circuit when the rate of change of flux is dФʙ / dt .)
37 - Induced emf set up across the ends of a conductor → ε = Blv ( ε is the induced emf set up across the ends of a conductor of length l when moving in a magnetic field B with a velocity v and in a direction perpendicular to B.)
38 - Faraday's law in general form → ε = ∮ E .dl ( E is a non conservative , time varying electric field that is produced by the changing magnetic flux .)
The essence of the law is that a changing magnetic flux induces an electric field.
ε = 1/2 B⍵l² ( ε is the emf induced in a rod of length l rotating with constant angular speed ⍵ in a uniform magnetic field .)
ε = NAB⍵sinθ ( ε is the induced emf in the rotating armature of a dynamo whose total number of turns is N ,area is A , B is the magnetic induction ,⍵ is the angular velocity and θ is the angle between B and A .)
39 - Current → I = (V - ε ) /R ( I is the current through the armature coil of a dc motor of resistance R . Here V is the applied voltage and ε is the back emf .)
40 - Efficiency of dc motor → 𝜼 = ε / V
41 - Self induction → L = Φʙ / I ( L is the self induction of the coil and Фʙ is the magnetic flux linked with it when a current I flows through it.)
42 - Coefficient of self induction → ε = L ( dl/dt) ( ε is the induced emf set up in a coil when the rate of change of current in the coil is dl/dt . L is the coefficient of self induction or self inductance or simply the inductance of coil . Inductance is the measure of the opposition of a device to a change in current.)
43 - Inductance of a solenoid → L = (μ₀N²A / l ) ( L is the inductance of a solenoid whose core is a vacuum ), N is the total number of turns , A is the cross sectional area and l is the length of a solenoid .)
44 - Mutual induction → Фʙ = MI ( M is the mutual induction of two coils , I being the current through one coil and Фʙ is the flux linked with the other coil.)
45 - Energy stored in the magnetic field of an inductor → Uʙ = 1/2 LI²
46 - Magnetic energy density → uʙ = B²/ 2μ₀ ( uʙ is the magnetic energy density at a point where the magnetic field is B . Thus the energy density is proportional to the square of the field at that point. )
Physics is about questioning , studying , probing nature .You probe and if you are lucky , you get strange...
well..!! wait for next session..till than bye bye..:)
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