Current Magnetic Effects
Magnetic field strength due to a straight finite current carrying conductor
B = μ0I/4πrd [cos∅2] = μ0 I/4πd [sin α - sin β]
The direction of magnetic field is given by right hand thumb rule.
Magnetic field at perpendicular bisector of a current carrying conductor
B = μ0 Ia/2πd a2 + 4d2
Magnetic field due to a long straight conductor
B = μ0I/2πd
Force between parallel conductors
dF/dl = μ0 l1l2/2πd
The force is attractive if the currents are in the same direction and repulsive if the currents are in the opposite direction.
Magnetic field at the centre of a circular loop carrying current
The direction is perpendicular inwards if the current is clockwise and perpendicular outwards to the plane of paper if the current is anticlockwise.
Magnetic fields due to a circular are of radius r at the centre p
B = μ0 I (α)/4π
Take α in radian
For a semicircular loop α = π2
B = μ0I/4r
Magnetic field at any point on axial line
B = μ0 Ir2/2 (r2 + x2) 3/2
Find the direction as for a circular coil.
Special case magnetic field at the centre (put x = 0)
B = μ0I/2r
Ampere circuital law
?B dl = μ0l
Magnetic field due to a long solenoid at the axis of a solenoid
B = nμ0l
Where n is number of turns per unit length
Magnetic force between tow current carrying conductors (long)
dF/dl = μ0 l1l2/(2πd)
The force is attractive if currents are in same direction and repulsive if currents are in opposite directions.
Magnetic field at any point p in the solenoid
Bp = 1/2 μ0nl (cos θi - cos θ2)
At point, f or E due to a long solenoid
B = 1/2 μ0nI
Magnetic field at any point p (acting tangentially) on a toroid
B = μ0Ni/2π
Where N = total number of turns
Magnetic field due to a moving charge
B = μ0qv sin∅/4π2 B = μ0q v x r/4πr3
Magnetic force between moving charges
F mag = μ0q1q2 (v1v2/4π2)
If the charges are like and move in same direction that they repel each other because F elec > F mag which is repulsive though magnetic force is attractive.
The force will be attractive only if the charges are of opposite nature.
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