Magnetic Effect of Electric Current

## Directions of Electric and Magnetic Fields

Motion : Thumb  ; Magnetic Field : First Finger ; Current : Middle Finger

## Force between two parallel conductors

*B* = (*µ0I1I2)*/(2π*a*)

Force experienced by a charge = qvBsinθ

Force experienced by a conductor in magnetic field = IBlsinθ

## Additional Configurations

1. Field due to two concentric coils of radii r1 and r2 having turns N1 and N2 in which same current I is flowing in anticlockwise direction at their common center O :-

```
        B = µ0 I/2 [N1/r1+ N2/r2]

```

( + if current is in same direction and - if opposite directions . )

2. Field due to semicircular arc of wire at the center *O* of the arc:-

* B = (*µ0* πI) / (4π*R*)

3. Field due to straight wire and loop at the center *O* of the loop (If the current in the looop in anticlockwise direction):-

B = (µ0 /4π) [2πI/R+ 2I/R]

4. Field due to semicircular concentric arcs of wire :

B = *µ*0*I*/4 [1/*a*-1/*b*]

5. Field due to 2 semicircles of radius R & r :

B = *µ*0*I*/4 [1/*R*+1/*r*]

## Ampere's Circuital Law

Ampere's Circuital Law states that the line integral of Magnetic Induction is equal to the product of absolute permeability and Current flowing through the coil . Magnetic Lines of Force are also referred to Amperian Loops .

∫ B.dl = μ0 I

## Galvanometer

A Galvanometer is used to measure a small current . Thus, a Galvanometer is mostly used to only detect the presence of current . To measure larger values of current , a galvanometer is converted to an Ammeter by connecting a Shunt resistance of low resistance in parallel to the galvanometer . A Voltmeter can be prepared from a galvanometer by adding a resistor of infinitely high resistance in series to the galvanometer .

## Moving Coil Galvanometer

A moving Coil Galvanometer consists of a soft iron core of high permeability , on which a rectangular coil is wound . The coil is then placed between the poles of a strong magnet . The coil rotates with a change in Current ... **i α θ**

**Suspended**

The coil is suspended from a rigid support . On the suspension cable , there is a mirror . Light is made to fall on the mirror . When the deflection begins , the reflected ray moves along a calibrated scale . This measures the current .

**Pivoted**

The coil is pivoted from both ends . The top end of the coil is connected to a pointer , which moves with deflection in the coil . The pointer is then pointed on a semi-circular scale .

The pivoted set-up is easier to handle than the suspended set-up .

## Ammeter

To measure larger values of current , a galvanometer is converted to an Ammeter by connecting a Shunt resistance of low resistance in parallel to the galvanometer .

The maximum current measured by galvanometer is called as Galvanometer Current (ig) or Full scale deflection . When shunt is connected , only a fraction of current flows through the galvanometer . For e.g. consider a Galvanometer of Full Scale Deflection 10 mA . Suppose the range of Ammeter is increased to 100 mA . Now if 50 mA Current is flowing through the Ammeter , 5 mA will flow through Galvanometer and 95 mA will flow through Shunt . Thus , the galvanometer reading will be 5 . But , since 10 mA was increased to 100 mA (10 times ) the least count also changes . Now , the least count is 10 mA as opposed to 1 mA initially . Thus the reading is 5 and the value of Current measured is 50 mA .

The shunt resistance should be of lower resistance , so that most current flows through the shunt . The Shunt resistance should be decreased to increase the range of an Ammeter .

## Voltmeter

A Voltmeter can be prepared from a galvanometer by adding a resistor of infinitely high resistance in series to the galvanometer . The added resistance provides a huge potential drop , which is required to measure the potential difference .

To increase the range of voltmeter , the resistance should be increased .

## Cyclotron

Cyclotron is an instrument used to accelerate a positively charged particle .

The cyclotron consists of two hollow semi-cylindrical metal boxes . These are called as 'dees' . There s a gap between the dees . The dees are kept under a strong magnetic field . A potential of the order 106  V is applied between the dees and high frequency of 107 Hz .

The particle is kept in the gap . Due to high frequency of Alternating voltage , the dees keep switchng their polarities . If D1  is at negative potential at first , the charged particle moves away from D2 . This force acting on the charge due to magnetic field provides necessary centripetal force . This force helps the charge to be accelerated and moves towards the gap between the dees .

**r = mv/ qB**

**t = 2mπ / qB = 2πr / v**

**f = 1/t = qB / 2πm**

**vmax = qBR / m**

**K.E. = q2B2R2 / 2m**

## Tangent Galvanometer

B = BHtanθ

μ0ni / 2r = BHtanθ