Download Force in Magnetic field :-

Force in Magnetic field :The force acting on a conductor kept in a magnetic field
is given by
fm = BIL
Where, fm = Force acting on the conductor, N.
B = Magnetic flux density Wh / m2
I = Current in the conductor, A
L = Length of the conductor, m;
→ The direction of the force is perpendicular to the plane
consisting of the components B & I that are mutually
perpendicular.
→ If an electron takes “ T ” Seconds to travel a distance of “ L ”
metres in the conductor, the total number of electrons passing
through any cross-direction of conductor in unit time is N / T,
Where
“ N ” is the total number of electrons contained in the conductor.
Thus the total change per second crossing any point (ie)
The current is I = Nq / T
Fm = BIL = BNq .L / T
→ The factor L / T is the different speed V, m/ s of the electrons
Hence, the force per electron is
Fm = q.BV
→ If the particle is a positive ion, the direction of current
different velocity are the same.
→ If the particle is electron, the direction of current is opposite
that of the different velocity.
Motion in a Magnetic field :The magnetic force acting on a changed particle in a
uniform magnetic field can be expressed as
—
—
—
fm = q. B x V
fm = q.BV sinφ
Where, φ = Angle b / w the direction of the Magnetic field
and the direction of the motion of changed particle.
→ From equation 1 we can say that the magnitude of the
magnetic force is proportional to the change of the particle, the
magnitude flux density, the speed of the changed particle and the
angle between the directions of motion of a changed particle and
the magnetic flux density.
→ If an electron is placed in a uniform magnetic field with zero
initial velocity, then the magnetic force on the electron is zero;
˙ ˙
. fm = qB.V sinφ ;
if V = 0; fm = 0;
→ In Accordance with eqn 1; The electron along the direction of
magnetic flux density, then the angle will be few;
fm = q.B.V sinφ
if , φ = 0 ;l then fm = q.B.Vsin0
˙ ˙
fm = q.B.V(0);
. sin0 =0
fm = 0
→ A particle whose initial velocity has no component normal to
a uniform magnetic field will continue to move with constant
velocity since the magnetic force on the particle is zero.
→ The magnetic force acting on a electron moving
perpendicularly is the direction of the magnetic flux density is
q.BV
since, fm = q.B.V.sinφ
fm = q.B.V.sin90• = q.B.V. (1)
fm = q.B.V.
Motion of an electronin a Magnetic field
 The electron enters to the magnetic field from no
field region with an initial velocity V0. At every
point in the magnetic field, force acts on the electron
and the resultant directions will be perpendicular to
both the magnetic field and the direction of motion
of electron at that point;
 At every Instant the force “ fm ” is perpendicular to
the direction particle. This will change the path taken
by the changed particle shown in figure. (ie) This
type of force makes an electron to move in circular
path.
 Here this magnetic force is the same as the
centripetal force which always tries to push the
electron towards the centre.
Then,
mv2 / r = q.BV ;
Where, r – Radius of the
circular path of the electron.
r = mv2 / q. BV = mv / q.B
r = mv / q.B
Angular velocity of the electron in radius / second is
given by
w = V / r = qB / m
w = qB / m
The time for one revolution is
T = 2π / w = 2πm / qB
T = 2πm / qB