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Forces between two parallel infinitely long current-carrying conductors:

Magnetic Field on RS due to current in PQ is

Force acting on length l of RS due to current I₂ is

Magnetic Field on PQ due to current in RS is

Force acting on length l of PQ is

Force per unit length of the conductor is,

I₁

I₂

F₂₁

F₁₂

B₁

B₂

N/m

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Definition of Ampere

Force per unit length of the conductor is

When I₁= I₂ = 1 Ampere and r = 1 m, then

One ampere is that current which passing through two parallel conductors of infinite length and placed 1 m apart in vacuum exerts a force of 2 x 10^-7 Newton per metre on each other.

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Torque on a rectangular current loop in Uniform Magnetic field

Force on PQ is,

Force on RS is,

Torque = Force x ⊥ distance

Here θ the angle between B and is 90^o.

The forces are equal in magnitude and opposite in direction separated by perpendicular distance.

In ◺OPS,

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Magnetic dipole moment of a circular current loop

Consider a circular loop of area A and carrying a current I.

Then it will act like a magnetic dipole.

The magnetic dipole moment(m) is given by,

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The magnetic dipole moment of a revolving electron

Current due to motion of electron,

Magnetic dipole moment,

From Bohr’s Second postulate,

For n = 1,

Bohr magneton .

Its value is 9.27 x 10^-24Am².

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Moving Coil Galvanometer

Principle

A current carrying rectangular loop placed in an external magnetic field experiences a torque.

T – Torsion Head, TS – Terminal screw, M – Mirror, N,S – Poles pieces of a magnet, LS – Levelling Screws, PQRS – Rectangular coil, PBW – Phosphor Bronze Wire

A moving coil galvanometer is a device used to detect electric current in a circuit.

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Torque experienced by the coil is,

Restoring torque in the coil is,

where k is restoring torque per unit angular twist.

At equilibrium,

Where G = Galvanometer constant

In a radial field θ will be always 90^o, hence the deflecting torque on the coil is,

Let φ be the angular twist of the wire.

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Current Sensitivity

Current sensitivity of the galvanometer is defined as the deflection per unit current .

Voltage Sensitivity

Voltage sensitivity is defined as the deflection per unit voltage.

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Conversion of Galvanometer to Ammeter

A galvanometer is converted to ammeter by connecting a low resistance S called shunt resistance in parallel to it.

I_g

I - I_g

The potential difference across galvanometer and the shunt are equal.

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Conversion of Galvanometer to Voltmeter

A galvanometer is converted to voltmeter by connecting a high resistance R in series to it.

Potential difference to be measured is the sum of p.d across galvanometer and p.d. across the high resistance.

I_g