MOVING CHARGES AND MAGNETISM
1. dB = µ0 / 4π ( I dl sin ᴓ / r2
) [ Biot – savart’s law ]
2. B = µ0 I / 4πa [sin ᴓ1 + sin ᴓ2
] [ Magnetic field due to a long
straight
current carrying conductor ]
3. B = µ0 I / 2πa
[ When point lies near the centre of conductor ]
4. B = µ0 I / 4πa
[ When point lies near the end ]
5. B = µ0 I / 2r [ Magnetic field at the centre of
circular current loop ]
6.
B = µ0 I a2 / 2(r2
+ a2)3/2 [Magnetic
field on the axis of a circular current loop]
7. Ampere’s law:
Ampere’s circuital law states that the
line integral of magnetic field B
around any closed circuit is equal to µ0 times the total current
“ I “ passing through this closed circuit.
ʃ B. dl = µ0 I
Here B = Magnetic induction
µ0 = permeability of free
space
I = Current
8.
Cyclotron – It is a device use to accelerate charge particles like
protons, deuterons, α – particles etc. to very high energies.
9.
r = mv / q B
Here
m = mass of the particle
V = velocity of particle
q = charge
B = magnetic induction
10.
T = 2πm / q B Here
T = Time period
11.
If the frequency of the applied voltage is kept exactly the same as the
frequency of revolution of the proton, then every time the proton reaches the
gap between the two dees, the electric field is reversed and proton receives a
push and finally it acquires high energy. This is called cyclotron’s resonance
condition.
12. f c = 1 / T = q B / 2πm Here f c = Cyclotron
frequency
13. K = q2 B2 r02
/ 2m
Here K = Maximum Kinetic Energy
14. Limitations –
·
Electrons can’t
be accelerated in a cyclotron.
·
Neutrons, being
electrically neutral, can’t be accelerated in a cyclotron.
15. F = q v B sin ᴓ = q (v x B) [Force on a moving charge in a magnetic field]
Here q = charge
V = velocity
B = Magnetic Induction
16. Fleming’s left hand rule –
Federal Bureau of India – F B I (Trick for
Remember)
F – Direction of Force – Thumb
B – Direction of Magnetic field – Fore finger
I – Direction of current – Central finger
17. Lorentz Force –
F = F e + F m
= q [E + (V X B)]
Here E = Electric field
V = Velocity
B = Magnetic induction
18. F = I (L x B) = I L B sin ᴓ [Force
on a conductor carrying current
and placed in a
magnetic field]
Here I = Current
L = length of conductor
B = Magnetic induction
19. F = µ0 I1 I2
L / 2πr
20. Moving coil galvanometer is an
instrument used for detection and measurement of small electric current.
21. I = G ᴓ
Here k / n B A = G = Galvanometer
constant
22. Current sensitivity of a
galvanometer is defined as the deflection produced in the galvanometer when a
unit current flows through it.
I s = ᴓ /
I = N B A / k
Here N = Number of turns
B = Magnetic Induction
A = Area
K = Restoring torque
23. The S.I. unit of current
sensitivity is radian ampere-1.
24. Shunt is a low resistance
connected in parallel with the galvanometer or ammeter.
25. I s = I (G/G+S)
Here I = Current
G = Resistance of galvanometer
S = Resistance of shunt
26. USES –
v A shunt is used to protect the galvanometer
from strong current.
v A shunt is used for converting a galvanometer
into an ammeter.
v A shunt may be used for increasing the range
of ammeter.
27. Ammeter –
v An ammeter is a low resistance galvanometer.
It is used to measure the current in a circuit.
v A galvanometer can be converted into an
ammeter by using a low resistance wire in parallel with the galvanometer.
v S = ( I g / I - I g
) G
Here
G = Resistance of galvanometer
I = Current
I g = Current through
galvanometer
28. Voltmeter –
v A voltmeter is a high resistance galvanometer.
It can be used to measure the potential difference between any two points of a
circuit.
v A galvanometer can be converted into a
voltmeter by connecting a high resistance in series with the galvanometer.
v R = V / I g – G
Here V =
Potential difference
I g = Current through
galvanometer
G = Resistance of galvanometer
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