CLASS 12 MOVING CHARGES AND MAGETISM
MOVING CHARGES AND MAGNETISM
✤ Magnetic Field (B) [MT-2A-1]
The space around a magnet within which its influence can be experienced is called its magnetic field.
- Vector quantity.
Unit is TESLA, OERSTED
❈ Oersted's experiment
A current carrying conductor produces a magnetic field around it.
1. It is the experimental verification of magnetic field
❈ Biot-Savart Law
State that B produce by a straight current carrying conduction is always proportional to current element, sin of the angle & inversely proportional to the distance square
dB = μ₀/4π. Idlsinθ/ r2 (Tesla)
Special Cases:
θ = 0°, sinθ = 0, ∴ dB = 0 & θ = 90°, sinθ = 1, ∴ dB= max
1. It is valid for a symmetrical current distribution, small conductor
2. It is the analogous to coulomb's law.
3. direction of dB is ⊥ to both Idl and r
Magnetic Field due to a long straight current carrying conductor:
B= μ₀I/4πa [sinφ₁ + sinφ₂]
Special Case Φ₁ = Φ₂ = 90° & Φ₁ = 90° Φ₂ = 0°
B= μ₀I/2πa for infinitely long I wire
Notes :
long wire i
B= MoI / 4πa
B = M0 NI/2π→ for circular current carrying loop
B = Mot/4π →semi conductor loop
Direction of magnetic field
i) If I is in upward direction them B is anticlockwise.
ii) If I is in downward direction then B is clockwise.
❈ Right hand thumb rule. (maxwell's law):
If we hold the straight conductor in the grip of our right hand in such a way that the extend thumb points in the direction of current, then the direction of the curl of the fingers will give the direction of the magnetic field.
Magnetic Field at the centre of circular current loop
B= μ₀I / 2a ---- distance
For N turns 1. B= B₁+B₂
B= μ₀NI / 2a 2. If current is opp. direction
then B= B₁- B₂
3. 
may-field by arc
may-field by arc B=μ₀/4π . I/r . θ
4. 
B = √B₁²+B₂²
B = √B₁²+B₂²
❈ Magnetic Field on the axis of a circular current loop
B = μ₀ I a² / 2 (r² + a²)³/2
• For N turns
B = μ₀ N I a² / 2 (r² + a²)³/2
Special Case : i> Centre of current loop, n = 0
B = μ₀ N I A / 2πa³
ii> At the axial points lying far away from the coil.
B = μ₀ I N a² /2r³ = μ₀ N I A / 2πr³
iii> At an axial point at a distance equal to the radius of the coil.
B = μ₀ N I a² / 2(a² + a²)³/2 = μ₀ N I / 2⁵/²a
❈ Force on a moving charge in a magnetic field.
F = q v B sin θ (Newton)
Special Case i) v = 0 then F = 0 (in. Rest No Force)
ii) θ = 0° or 180° then F = 0
iii) θ = 90° then F = q v B sin 90°
F = q v B
Where F is ⊥ to v & B
Rules for finding the direction of force on a charged particle moving perpendicular to a magnetic
--- Right hand (palm) rule.
Open the right hand & place it so that tips of the fingers point in the direction of the field B and thumb in the direction of velocity of the positive charge, then the palm faces towards the force F
Note : Static charge is a source of Electric field but not magnetic field whereas moving charge is a source of electric and magnetic field.
Force on a current carrying conductor in a magnetic field
F = Il B sin θ
Special Case : i> 0=0° or 180° 
ii> 0=90°
ii> 0=90°
F= I l B (0) Fmax = IlB
F=0
Force b/w 2 parallel current carrying conductors
F12 = F12/l - μ₀I1I2/2πr
For length ‘l’
F12 = μ₀I1I2/2πr
§ 1> F12 = F211
2> If direction of current is same then force is Attracts.
3> If direction. is opp. then force is repulsive.
1. Force of PQ = μ₀2I1I2/4π A X PQ
2. Force of RS = μ₀2I1I2/4π (A+B) X RS
3. Total force = Fpq - FAB
❈ Define 1 Ampere
1 Ampere is the current which when flowing into 2 Parallel conductors placed at 1m distance in vacuum produce 2 X 10-7 N force (attractive or repulsive) at unit length of the wire.
❈ Ampere's Circuital Law
States that line integral of magnetic field around a close loop is
muo times the total current passing through the loop.
B dl = μ₀ . I
Application of Ampere's Circuital Law
i> Magnetic field due to long current carrying wine.
B = μ₀I/2πr
ii> Magnetic field due to a current carrying solenoid, at middle.
B= μ₀ nI (n=N/2)
iii> at the ends of solenoid
iv> magnetic field by toroid
1) inside and outside
B=0
2) only in the brim
B= μ₀NI/2πr
Note: Variation in magnetic field by solenoid
Torque Experienced by a current loop in a uniform magnetic field.
τ = IBAsinθ
For N turns
τ = NBAsinθ
τ = mBsinθ
Special : i> θ = 0°
Here M=NIA
Case then τ = 0 (minimum) τ = M × B
ii> θ = 90°
then, τ = NIBA (max)
iii> direction of torque is always ⊥ to M and B
For your knowledge
1 - Torque is max when the loop is circular in shape.
2 - If the direction of the magnetic field makes an angle α with the plane of the current loop
θ + α = 90° or θ = 90° - α
τ = NBAsin(90°-α) = NIBA cosα
3 - In uniform 𝐵, the net magnetic force on a current loop is zero, but to τ may be zero or not.
4 - In non-uniform 𝐵, the net magnetic force on a current loop is non-zero, but τ may be zero or not.
5. direction of 𝑖𝑑 is out ward if current is anticlock. otherwise inward in clockwise.
✤ Moving Coil Galvanometer
Galvanometer is a device to detect current in a circuit.
Principle => Current carrying coil placed in a magnetic field experience a torque, the magnitude of which depends on the strength of current.
k = NIAB/θ A =Area of coil.
k = Restoring torque in P. Bronze wire because it has small restoring torque per unit
→ high tensile strength.
Galvanometer Constant/ Figure of merit
Current required for unit deflection
G = I / θ = k / θ NAB
Sensitivity of a galvanometer.
It is said to be sensitive if it shows large scale deflection even when a small current is passed through it or a small voltage is applied across it.
Current Sensitivity
Deflection per unit current
Ts = θ /I = NBA/k = Is
Voltage sensitivity
Deflection per unit voltage
Vs = θ / v = NBA / kR
Vs ∝ IR R = Resistance of copper coil.
Factors sensitivity of a moving coil galvanometer depends:
i) No. of turns N in its coil Res sensitivity ↑es.
ii) Magnetic field ↑es sensitivity ↑es.
iii) Area of the coil ↑es sensitivity ↑es
iv) Torsion constant k of the spring and suspension wire ↓es sensitivity ↑es.
For your knowledge : →
- Phosphor bronze is used for suspension on hair springs because : -
i) good conductor of electricity.
ii) does not oxidise.
iii) very little elastic after effect.
iv) perfectly elastic.
v) non-magnetic.
vi) smallest torsion constant k.
→ Iron core is used in galvanometers to increase its sensitivity by strengthening of the magnetic field line in the core as the no. of the turns are increased in the core.
→ Spring is used to produce restoring torque & hence helps in producing a steady angular deflection
→ Radial magnetic field ump → max torque is produced & torque is uniform in all the position of moving coil galvanometer.
❈ Conversion of Galvanometer in Ammeter
An ideal ammeter has negligible resistance ammeter is connected in series combination.
-> By connecting a low resistance (shunt) is parallel combination to the galvanometer. It can be converted into an ammeter.
VS = VG
(I - Ig)S = Ig x G
S = Ig / (I – Ig) x G
Resistance of ideal A is zero. R = GS / G+S
Notes :- 1. The range of A char can be ↑ but not ↓
2. Ammeter of lower range has higher resistance than A of higher range
3. A can't be connected in parallel, because resistance of the circuit ↓, current ↑ as a result A get damaged.
4. If ammeter range to be increased 'n' times its original value, the shunt should be s = G / n-1
❈ Conversion of Galvanometer into Voltmeter
An ideal voltmeter has infinite resistance. Voltmeter is connected in parallel combination.
-> By connecting a high resistance in series combination.
V = VG + Vr
V = Ig x G + Ig R
V = Ig (G + R)
V / Ig - G = R
Note: 1. The range of V can be ↑ or ↓ 2. A of lower range has lower resistance than V of higher range.
2. If V is connected in series, resistance of circuit become high and current ↓ now voltmeter measure the emf of battery.
3. If A range is to be increased to 'n' times its original values then resistance should be connected R = (n-1) G
4. Resistance of ideal V is infinite.
Note:
+ve charge makes
anticlock rotation.
1. Neg-charge particle makes anticlock wise rotation and radius r = mV/qB and time taken to come out of B, t = πr / V
t = 2π m / qB
U=½ q² . B²/m . r²
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