1. Biot Savart Law

d

**B**= [1/4 π ε

_{0}c²]*(i) (

**dl***

**r**/r³) ... (1)

where

dB = magnetic field at point P, due to current element dl

c = speed of light

i = current

r = vector joining the current element to the point P.

[1/ ε

_{0}c²] is written as µ

_{0}and is called the permeability of vacuum.

Its value is 4 π*10

^{-7 }T-m/A

In terms of µ

_{0}equation (1) becomes

d

**B**= (µ

_{0}/4 π)*(i) (

**dl***

**r**/r³) ... (2)

The magnitude of the field

dB = (µ

_{0}/4 π)*(idl sin θ/r²)

where θ is the angle between dl and r.

the direction of the field is perpendicular to the palne containing the current element and the point P according to the rules of the cross product.

4. Magnetic field due to current in a straight wire

B = (µ

_{0}i /4 πd) (cos θ1 – cos θ2) … (4)

θ1 and θ2 and the value of θ corresponding to the lower end and the upper end respectively.

If the point P is on the perpendicular bisector of the straight wire

B = (µ

_{0}i /4 πd) [2a/√(a² +4d²)] … (5)

a = length of the wire

d = distance between the wire and point P (perpendicular distance)

If the wire is very long such that θ1 = 0 and θ2 = π.

The equation is B = (µ

_{0}i /2 πd) … (6)

7. Force between two parallel currents

dF/dl = (µ

_{0}i

_{1}i

_{2})/2 πd

dF/dl = force per unit length of the wire W2 due to wire W1

i

_{1},i

_{2}= current in wire W1 and W2 respectively

d = distance between wires kept parallel to each other.

8. Magnetic field in an axial point

B = (µ

_{0}ia²)/[2(a²+d²)

^{3/2}] .. (8)

If the point is far away from the centre d is very large compared to a

B = (µ

_{0}ia²)/2d³

If the magnetic dipole moment of due to the circular conductor with area πa² and current flowing through it is ‘i’, the µ = i πa² and B is

**B**= (µ

_{0}i /4π)(2

**µ**/d³) .. (9)

10. Ampere’s law

The circulation of ∫B.dl of the resultant magnetic field along a closed plane curve is equal to µ

_{0}times the total current crossing the area bounded by the closed curve provided the electric field inside the loop remains constant.

The circulation ∫

**B**.

**dl**over closed curve = µ

_{0}*I … (10)

11. Magnetic field inside a solenoid

B = µ

_{0}ni

n = number of turns per unit length along the length of the solenoid.

i = current passing through the solenoid

12. toroid

B = µ

_{0}Ni/2πr

Where

N = total number of turns

i = current in the toroid

r = distance of the point at which field is being calculated from centre of the toroid.

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