Moving Charges-02

William Doyle A F

PGT Physics

Magnetic Effect of Current – Oersted’s Experiment

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Oersted’s Experiment:

When current was allowed to flow through a wire placed parallel to the axis of a magnetic needle kept directly below the wire, the needle was found to deflect from its normal position.

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When current was reversed through the wire, the needle was found to deflect in the opposite direction to the earlier case.

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Rules to determine the direction of magnetic field:

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Right Hand Thumb Rule

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Imagining to hold the conductor in right hand such that the thumb is the the direction of current then the folded fingers show the direction of magnetic field.

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Maxwell’s Cork Screw Rule or Right Hand Screw Rule:

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If the forward motion of an imaginary right handed screw is in the direction of the current through a linear conductor, then the direction of rotation of the screw gives the direction of the magnetic lines of force around the conductor.

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Biot – Savart’s Law:

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The strength of magnetic field dB due to a small current element dl carrying a current I at a point P distant r from the element is directly proportional to l, dl, sin θ and inversely proportional to the square of the distance (r²) where θ is the angle between dl and r.

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Biot – Savart’s Law in vector form:

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Direction of dB is same as that of direction of dl x r which can be determined by Right Hand Screw Rule.

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Current element is a vector quantity whose magnitude is the vector product of current and length of small element having the direction of the flow of current. ( I dl)

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Magnetic Field due to a Circular Loop carrying current:

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1) At a point on the axial line:

Magnetic field at P due to current element at A

Magnetic field at P due to current element at B

Net magnetic field at P is,

But,

Also in △OAP,

Let N be the number of turns of coil.

At the centre of loop, x = 0

2) B at the centre of the loop:

Ampere’s Circuital Law

The line integral of magnetic field around a closed loop is equal to μ₀times the total current passing through the loop.

Magnetic field due to a infinite straight current carrying conductor

I

B

r

P

According to Ampere’s Circuital law

But,

Magnetic Field at the centre of a Straight Solenoid

Magnetic field due to a Toroid

The magnetic field exists only in the tubular area bound by the coil and it does not exist in the area inside and outside the toroid.

i.e. B is zero at O and Q and non-zero at P.

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Let n = no of turns per unit length

Ampere’s Circuital Law,