Moving charges and Magnetism 2

Question 1

force experienced by a moving charge in a magnetic field

Answer 1

• statis charge does not experience any force
• if the angle between the velocity of the charge and the magnetic field is 0/180, no force is expereinced by the charge
• Since the force is perpendicular to the velocity, the work done is 0
• the magnetic force is perpendicular to the velocity so it can only change the directio, but no change in the magnitude ie speed.

F= q( v x B)
=qvBsinq

Question 2

what is one tesla

Answer 2

The strength of the magnetic field at a point is said to be 1 Tesla, if a moving charge moves at a right angle to the field with a velocity 1 m/s experiences a force of 1N.

Tesla is a rather large unit. A
smaller unit (non-SI) called gauss (=10–4 tesla) is also often used. The
earth’s magnetic field is about 3.6 × 10
–5 T.

Question 3

what happens when a charge moves parallel or antiparallel to the mag field

Answer 3

The particle will continue moving along the same direction with the same velocity, because sinq=0
it will continue uniform motion in a straight line.

Question 4

what happens when a charge moves perpendicular to the field

Answer 4

the case of v perpendicular to B. The
perpendicular force, q v × B, acts as a centripetal force and
produces a circular motion perpendicular to the magnetic field.
The particle will describe a circle if v and B are perpendicular
to each other.

r=mv/qB
T= 2πm/qB

r depends on velocity but T doesnt.

Question 5

what happpens when a charge moves at an angle theta to the field.

Answer 5

If velocity has a component along B, this component
remains unchanged as the motion along the magnetic field will
not be affected by the magnetic field. The motion in a plane
perpendicular to B is as before a circular one, thereby producing
a helical motion

the velocity can be resolved iinto mutually perpendicular directions vcosq and vsinq,

vcosq is parallel to the mag field. The force on charged particle is 0. hence, it will move in a uniform motion along the direction of B.

vsinq is perpendicular to B. Force on the particle is qvBsinq. This force with act as centripetal force and charged particle will move in the circular path of radius
r=mvsinq/qB

under the combined effect of both the components, the path of the charged particle will be helical.

Question 6

what is the pitch?

Answer 6

The horizontal distance travelled by the chaged particle in one time period is called the pitch.
P= vcosq x T

Question 8

Lorentz force

Answer 8

F = q [ E (r) + v × B (r)] = Felectric +Fmagnetic

It is called the Lorentz force.

(i) It depends on q, v and B (charge of the particle, the velocity and the magnetic field). Force on a negative charge is opposite to that on a positive charge.

(ii) The magnetic force q [ v × B ] includes a vector product of velocity and magnetic field. The vector product makes the force due to magnetic field vanish (become zero) if velocity and magnetic field are parallel or anti-parallel. The force acts in a (sideways) direction perpendicular to both the velocity and the magnetic field.

(iii) The magnetic force is zero if charge is not
moving (as then |v|= 0). Only a moving
charge feels the magnetic force.

Question 9

unit of magnetic field and dimensions

Answer 9

[B] = [F/qv] and
the unit
of B are Newton second / (coulomb metre). This unit is called tesla (T)
named after Nikola Tesla (1856 – 1943). Tesla is a rather large unit. A
smaller unit (non-SI) called gauss (=10–4 tesla) is also often used. The
earth’s magnetic field is about 3.6 × 10
–5 T.

Question 10

force on 2 parallel current carrying conductors

Answer 10

Fba = –Fab (4.18)
Note that this is consistent with Newton’s third Law. Thus, at least for
parallel conductors and steady currents, we have shown that the
Biot-Savart law and the Lorentz force yield results in accordance with
Newton’s third Law*

Parallel currents attract, and antiparallel currents repel

Question 11

define 1 ampere

Answer 11

The ampere is the value of that steady current which, when maintained
in each of the two very long, straight, parallel conductors of negligible
cross-section, and placed one metre apart in vacuum, would produce
on each of these conductors a force equal to 2 × 10–7 newtons per metre
of length.

Question 12

difference between magnetic and electric dipoles

Answer 12

a planar current loop is equivalent to a magnetic dipole of dipole moment
m = I A, which is the analogue of electric dipole moment p. Note, however,
a fundamental difference: an electric dipole is built up of two elementary
units — the charges (or electric monopoles). In magnetism, a magnetic
dipole (or a current loop) is the most elementary element. The equivalent
of electric charges, i.e., magnetic monopoles, are not known to exist.