FORCE ON A CHARGE IN A ELECTRIC FIELD :-
A charge q inside an electric field of strength E experiences force F is
[F] = [qE] = qE
MOTION OF A CHARGE INSIDE ELECTRIC FIELD :-
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
FORCE ON A CHARGE MOVING INSIDE A MAGNETIC FIELD :-
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.
LORENTZ FORCE:-
The total force experienced by a charge moving inside the electric and mag. field is called lorentz force
[F] = q[E + v * B]
MOTION OF A CHARGE INSIDE MAGNETIC FIELD :-
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 ( = 90o) 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 = 2
mvcos/Bq
CYCLOTRON FREQUENCY :-
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) Emax = 1/2 B2q2R2/m
where R is the radius of the dees of the cyclotron
b) Emax = 2N(Vq)
where N is the number of revolutions completed by the +ve ions before
leaving the dees
FORCE ON A CURRENT CARRYING CONDUCTOR PLACED INSIDE A MAGNETIC FIELD :-
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.
CURRENT SENSITIVITY :-
It is defined as the deflection produced in the galvanometer on passing a unit current through its coil.
Current sensitivity, /I = NBA/k
VOLTAGE SENSITIVITY :-
It is defined as the deflection produced in the galvanometer , when a unit voltage is applied across its coil
Voltage Sensitivity , /V = NBA/kR
AMMETER :-
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
S = Ig* G/I - Ig
here Ig is the max. current tht can pass through the galvanometer
The resistance of the ammeter so obtained is given by
RA = GS/G + S
An ammeter is a low resistance instrument and it is always conneted in series to the circuit
VOLTMETER :-
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/Ig - G
The resistance of the voltmeter so obtained is
RV = 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.
Notes :-
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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