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Moving Charges And Magnetism

Magnetic field due to current element, Biot-Savart; Magnetic field on the axis of a circular current loop

The magnetic effect of current was first discovered by H.C. Oersted. He observed that the flow of charges in a conductor produces magnetic effect around it. He demostrated this phenomenon using the experimental set-up shown below.

When the current in the circuit was anticlockwise, the magnetic needle was found to deflect towards West. The needle deflected towards East when the direction of current was reversed. This experiment proved that current has magnetic effect associated with it. 

The Biot–Savart Law

Let:

XY = Current-carrying conductor

I = Current in the conductor

dl = Infinitesimal element of the conductor

dB = Magnetic field at point P

r = Distance of point P from the element

According to the BiotSavart law, the magnetic field is proportional to the current and element length and inversely proportional to the square of the distance.

That is,

dB ∝

=

Here,

= Constant of proportionality =
10−7 Tm/A

μ0 = Permeability in free space

Magnetic field on the axis of a circular current loop

I = Current in the loop

R = Radius of the loop

X-axis = Axis of the loop

X = Distance between O and P

dl = Conducting element of the loop

  • According to the BiotSavart law, the magnetic field at P is

dB =

r2 = x2 + R2

|dl × r| = rdl      (Because they are perpendicular)

 

  • dB has two components: dBx and dB. dB is cancelled out and only the x-component remains.

dBx= dBcos θ

cos θ =

dBx =

  • Summation of dl over the loop is given by 2πR.
    B = =

  • For the magnetic field at the centre of the loop, x = 0.



Right-Hand Thumb Rule
Maxwell’s right-hand thumb rule indicates the direction of magnetic field if the direction of current is known.
According to this rule, if we grasp the current-carrying wire in our right hand such that our thumb points in the direction of the current, then the direction in which our fingers encircle the wire will tell the direction of the magnetic field lines around the wire.



When the thumb …

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