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MAGNETIC FIELDS AND ELECTROMAGNETISM

Law of Magnetic Poles:  Opposite magnetic poles attract.  Similar magnetic poles repel.
 


Magnetic Force on an Individual Moving Charge:

FM = q.v.B.sin Ɵ

FM:  Magnitude of magnetic force on moving charged particle (N)

q:  Charge on the moving charged particle (C)

v:  Velocity of the moving charged particle (m/s)

B:  Magnitude of magnetic field strength (teslas, T, kg/C.s)

Ɵ:  Angle between velocity vector (v) and the direction of magnetic field (B)

Use right hand rule to find the direction of the force.

Right-Hand Rule: By using your right-hand, point your right thumb in the direction of the positive charge.  Point your middle fingers in the direction of the magnetic field, B.  The force will be in the direction in which the right palm pushes.

Cross product of of current and magnetic field can be used to find out the direction of the force:  F = I x B

 

Magnetic force is both perpendicular to the velocity of the charge and the direction of the magnetic field.  Since FM is perpendicular to v, magnetic force acts as a centripetal force.  As a result, the charge particle travels in a circle.

How to find the radius of the circle:

Magnetic force in this situation provides centripetal force (net force):  FM = Fc

q.v.B.sin Ɵ = mv2/r

Since velocity (v) and the direction of magnetic is perpendicular each other, sin Ɵ = 1

q.v.B = mv2/r

r = (m.v) / (B.q)

 


Charge to Mass Ratio:

From above equation (r = (m.v) / (B.q), it is possible to calculate charge to mass ratio as given below:

General formula for charge to mass ratio:  q/m = v/(B.r)

FM = FE

q.v.B = q.Ɛ

v = Ɛ/B  (Substitute v into the formula q/m = v/(B.r)

q/m = Ɛ / (B2.r)

General formula for charge to mass ratio:  q/m = Ɛ / (B2.r) =  v/(B.r)

Charge to mass ratio for electron:  e/m = Ɛ / (B2.r) = v/(B.r) = 1.76 x 1011 C/kg

qvB = mv2/r    and   0.5mv2 = q∆V

isolate v in both

v = q.B.r/m  and v = (2qV/m)1/2

Mass of charge: m = (qB2r2)/(2∆V)

 


Magnetic Force on a Conductor:

 

F = k.I.L.B.sin Ɵ

k = 1

F:  Magnetic force on the conductor (N)

I:  Current on the conductor (amperes, A)

L:  Length of the conductor in the magnetic field (m)

B:  Magnitude of magnetic field strength (teslas, T, kg/C.s)

Ɵ:  Angle between current (I) and the direction of magnetic field (B)

Use the right hand rule to find the direction of the force.

 


Magnetic Force between two long, straight, parallel conductors:

F2:  Magnetic Force between two long, straight, parallel conductors (N)

L:  Length of the conductors (m)

I1:  Current on the first conductor (amperes, A)

I2:  Current on the second conductor (amperes, A)

d:  Distance between the conductors (m)

Proportionality constant (magnetic permeability of free space):  μ:  4π.10-7 (T.m/A) (for vacuum or for air approximately)

F2 / L = μ.I1.I2/(2πd)

If I1 and I2 are in the same direction, the conductors attract each other.  If the currents are in the opposite directions, the conductors repel each other.

 


Magnetic Field Strength around a Straight Conductor:

Proportionality constant (magnetic permeability of free space):  μ:  4π.10-7 (T.m/A) (for vacuum or for air approximately)

I:  Current on the conductor (amperes, A)

r:  Perpendicular distance from the straight conductor (m)

B = (μ.I) / (2πr)

 


Magnetic Field Strength in the Centre of a Flat Loop of Wire with N Turns:

N:  Number of loops in a flat coil of radius r

B = (μ.N.I) / (2r)

 


Magnetic Field Strength in the Centre of a Long Solenoid of Length L with N Turns:

N:  Number of loops

L:  Length of the solenoid (m)

B = μ.N.I / L