Magnetic Effect of Electric Current

Directions of Electric and Magnetic Fields
Right Hand Thumb Rule:

Fleming's Left Hand Rule :

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

Fleming's Right Hand Rule :

Motion :

Biot Savart's Law
B  = ( µ 0/4π) ( I  d l  sin  θ) /( r2 )

straight conductor
B  = ( µ0I) /(2π a )

Circular Conductor
B  = ( µ0I) /(2 a )

At a distance from circular conductor
B = µ0I a2 / (a2+x2)3/2

Force between two parallel conductors
B  = ( µ0I1I2) /(2π a )

Electric Force
Fq = qE

Force experienced by a charge = qvBsinθ

Magnetic Force
Fm = Q (vxB)

Electromagnetic Force
Fem= qE + q(vxB)

Force experienced by a conductor in magnetic field = IBlsinθ

Torque
Torque = MB sin θ

Additional Configurations
B = µ0 I/2 [N1/r1+ N2/r2] ( + if current is in same direction and - if opposite directions . )
 * 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 :-

2. Field due to semicircular arc of wire at the center  O  of the arc:- 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  πI) / (4πR)

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

Straight Conductor
B = μ0 I / 2πa

Solenoid
B = μ0NI

Torroid
B = μ0NI

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