Important formulas of magnetic effect of electric current
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Answer:
IMPORTANT FORMULAS OF MAGNETIC EFFECT;
Magnetic field: It is a region around a magnet or current carrying conductor in which its magnetic influence can be felt by a magnetic needle.
2. Biot‐Savart Law dB =μ0IdlSinθ/4πr2 μ0=4π x 10‐7 Tm/A [Direction of dB can be found by using Maxwell’s Right hand thumb rule.]
3. Applications : Magnetic field at a centre of a current carrying circular coil B= μ0I/2a
Magnetic field at a point on the axis of current carrying coil.
B= μ0Nia2/2(a2+x2)3/2 (N=no. of turns in the coil)
4. Ampere’s circuital law; It states that the line integral of magnetic field around any closed path in vacuum/air is μ0 times the total current threading the closed path. ∫ B. dl= μ0 I
5. Applications i) Magnetic field due to straight infinitely long current carrying straight conductor. B= μ 0 I/2πr
ii) Magnetic field due to a straight solenoid carrying current B= μ0n I n= no. of turns per unit length
iii) Magnetic field due to toroidal solenoid carrying current. B= μ0N I / 2πr N= Total no. of turns.
6. Force on a moving charge [ Lorentz Force]
(i) In magnetic field F=q(V x B)
(ii) In magnetic and electric field F=q[E+(ν x B)] Lorentz force
7. Cyclotron
(i) Principle (a) When a charged particle moves at right angle to a uniform magnetic field it describes circular path.
(b) An ion can acquire sufficiently large energy with a low ac voltage making it to cross the same electric field repeatedly under a strong magnetic field.
(ii) Cyclotron frequency or magnetic resonance frequency ν=qB/2πm, T=2πm/Bq; ω=Bq/m
(iii) Maximum velocity and maximum kinetic energy of charged particle. Vm=Bqrm/m Em=B2q2rm2 / 2m
8. Force on a current carrying conductor in uniform F= (I l x B) l=length of conductor Direction of force can be found out using Fleming’s left hand rule.
9. Force per unit length between parallel infinitely long current carrying straight conductors. F/l= μ0 I1 I2/2πd
(a) If currents are in same direction the wires will attract each other.
(b) If currents are in opposite directions they will repel each other.
10. 1 Ampere – One ampere is that current, which when flowing through each of the two parallel straight conductors of infinite length and placed in free space at a distance of 1m from each other, produces between them a force of 2x10‐7 N/m of their length.
11. Torque experienced by a current loop in a uniform
B. τ = NIBA Sinθ τ=MXB
Where M=NIA
12. Motion of a charge in
(a) Perpendicular magnetic field F=q(vxB),F=qvBSin90=qvB (circular path)
(b) Parallel or antiparallel field F=qvBSin0 (or) qvBSin180=0(Straight‐line path) If 0<θ<90 , the path is helix vCosθ is responsible for linear motion v, v Sinθ is responsible for circular motion Hence trajectory is a helical path
13. Moving coil galvanometer It is a sensitive instrument used for detecting small electric Currents.
Principle: When a current carrying coil is placed in a magnetic field, it experiences a torque.
I αθ andI = K θ where K= NAB / C
Current sensitivity, I s= θ / I=NBA/K
voltage sensitivity, Vs= θ /V=NBA/KR
Changing N ‐> Current sensitivity changes but Voltage Sensitivity does not change
(a) Conversion of galvanometer into ammeter A small resistance S is connected in parallel to the galvanometer coil
S=IgG/( I ‐ I g) ; RA=GS/(G+S)
(b) Conversion of galvanometer into a voltmeter. A high resistance R is connected in series with the galvanometer coil. R=( V/Ig) –G ; Rv=G+R Current loop as a magnetic dipole
Magnetic dipole moment
M = 2 evrM=n( eh / 4 πme)
14. Representation of uniform magnetic field. B
15. Magnetic dipole moment of a magnetic dipole.