A charge q inside an electric field of strength E experiences force F is

 

          [F] = [qE] = qE

 

 

If a potential difference V is applied b/w two parallel plates a uniform electric field is set up b/w the fields

 

          E = V/d

 

A charge q of mass m experiences force

 

          F = qE

 

The charge moves inside an electric field follows a parabolic path

 

 

A charge q moving with velocity v inside a mag. field of strength B is

 

          [F] = q[v * B] = Bqvsin

 

The charge does not experience any force if it is at rest or if it moves along the direction of mag. field.The force is max. when the charge moves perpendicular to the direction of mag. field.

 

 

The total force experienced by a charge moving inside the electric and mag. field is called lorentz force

 

          [F] = q[E + v * B]

 

 

A charge q of mass m moving with velocity v inside a mag. field of strength B experiences force

 

          [F] = q{v * B] = Bqvsin

 

where  is the angle b/w the direction of motion of the charge (v) and the direction of magnetic field (B). This force acts perpendicular to both v and B

 

a) If v and B are perpendicular ( = 90^o) the force on the charged particle makes 

    it to move along a circular path, whose radius is

         

          r = mvsin/Bq

 

b) If B and v act an angle  then due to the component of velocity v sin

    (perpendicular to B),the charged particle moves along a circular path

    of radius r

    

          r = mvsin/Bq

 

   while due to the component of velocity vcos (along B) the charged particle 

   at the same time moves along the direction of mag. field As a result the 

   charged moves along a helical path The pitch of the helical path is

 

         pitch = 2mvcos/Bq 

 

 

In a cyclotron the frequency of the applied alternating electric field is equal to the frequency of oscillation of the +ve ion and this frequency is called cyclotron frequency.

 

         = Bq/2m

 

where m and q are the mass and charge of the +ve ion and B is the mag. field

 

MAXIMUM ENERGY ATTAINED BY A POSITIVE IONS :-

 

a)     E_max = 1/2 B²q²R²/m

    where R is the radius of the dees of the cyclotron

 

b)     E_max = 2N(Vq)

 

    where N is the number of revolutions completed by the +ve ions before 

    leaving the dees

 

 

When two infinitely long parallel conductors carrying conductors carrying currents I₁ and I₂ are placed at a distance r apart then force per unit length of a conductor due to the other conductor is

 

          F = _o/4 .2I₁I₂/ r

 

The force is attractive if the currents in two conductors is in the same direction and repulsive if the currents are in the opposite directions.

 

TORQUE ON A CURRENT CARRYING COIL PLACED INSIDE A MAGNETIC FIELD :-

 

When a coil of area A having N turns and carrying a current I is suspended inside a mag. field of strength B then torque is

 

            = nBIAsin 

 

where  is the angle b/w the direction of mag. field and normal to the plane of the coil.

 

If the direction of mag. field makes an angle  with the plane of the coil then

 

            = nBIAcos

 

The torque on the coil is max. when the plane of the coil is parallel to the mag. field i.e.  = 90 or  = 0

 

SENSITIVITY OF A GALVANOMETER :-

 

A galvanometer is said to b sensitive if it gives a large deflection even when a small current is passed through it or when a small voltage is applied across its coil.

 

 

It is defined as the deflection produced in the galvanometer on passing a unit current through its coil.

 

 

 

It is defined as the deflection produced in the galvanometer , when a unit voltage is applied across its coil

 

Voltage Sensitivity , /V = NBA/kR 

 

 

Used to measure current

A galvanometer of resistance G can b converted into an ammeter of range I by putting a small resistance S in parallel to its coil

 

here I_g is the max. current tht can pass through the galvanometer

 

The resistance of the ammeter so obtained is given by

 

          R_A = GS/G + S

An ammeter is a low resistance instrument and it is always conneted in series to the circuit

 

 

It is an instrument used to measure potential difference across a conduator in an electrical circuit

 

A galvanometer of resistance G can b converted into a voltmeter to read upto V by connecting a large resistance R in series to its coil

 

         R = V/I_g - G

 

The resistance of the voltmeter so obtained is

 

         R_V = G + R

 

A voltmeter is a high resistance instrument and it is always connected in parallel to the conductor across which potential difference is to be measured.

 

 

1. A stationary charge experiences force inside an electric field. A mag. field

    does not exert any force on a stationary charge.

 

2. The experession for torque on a current carrying coil i.e.

    

     = nBIAsin 

   

    holds for a planar loop of any shape having the area A.

 

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