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We can imagine a magnetic field surrounding a magnet in much the same way that we did for electrical charges. •
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One of the biggest differences is that (a negative charge can be sitting all alone), while (north and south) Did You Know? There are some theories in modern physics that indicate that it should be possible (even though never been done) to isolate a north pole from a south pole. The dipoles would become monopoles. Similarities and differences
Strong field Not directly calculated in Physics (although we do measure it indirectly) Attraction or Repulsion
Weakest of all fields
Strong field.
Calculated using an Calculated using an inverse square law (Newton's inverse square law ) ( ) Universal Law of Gravitation Coulomb's Law Always attraction
Attraction Repulsion.
or
Directly related to the magnet Directly related to the involved masses involved
Directly related to the charges involved
Individual poles can never be separate from each other
Individual masses are separate from each other
Individual charges are separate from each other
Follows inverse square law near the magnet but follows an inverse cubed law further away so that the field becomes exponentially weaker as separation increases
Follows inverse square law so that the field becomes exponentially weaker as separation increases
Follows inverse square law so that the field becomes exponentially weaker as separation increases.
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Magnetic field exerts force on a charge particle
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a) From a point P, a charged particle can move in any direction or along any line. Along one of these possible lines, if the charge is moving, there is no magnetic force. Magnetic force is defined to be acting along this line. b) The magnitude of the magnetic force is proportional to the product of speed of the charged particle and , being the angle the speed makes with the line along which magnetic field is acting. Hence magnetic force is proportional to | |. c) The direction of the magnetic force is perpendicular to the direction of the magnetic field as well as to direction of the velocity. d) The magnetic force is also proportional to the magnitude of charge . e) Its direction is different and opposite for positive and negative charges. Magnetic force can be defined mathematically as � ⃗ = ⃗ × � from the rules of the vector product. Equation uniquely determines the direction of magnetic field •
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A magnetic field can create a force on an object. However, for the object to feel a force, and the magnetic field to affect the object, three things must be true 1. The object must have an electric charge. 2. The charged object must be moving. 3. The velocity of the moving charged object must have a component that is
to the
direction of the magnetic field. •
The SI unit of magnetic field is / − . It is written as . is / − . Tesla is also defined as /².
Another unit in common use is . 1 = 104 • • •
We have magnetic field of the order of 10−5 near the earth's surface. Superconducting magnets can create a magnetic field of the order of 10 . Earlier, the concept of magnetic field was referred to as magnetic induction.
Electric field and magnetic field are not basically independent. They are two aspects of same entity electromagnetic field. Whether the electromagnetic field will show up as an electric field or a magnetic field or a combination depends on the frame from which we are looking at the field. We represent magnetic field vectors like that as arrows. But all we see is either the tip of the arrow ⊙, if the field is coming out of the page, or the tail of t he arrow, ⊗, if the field is going into the page. Magnetic force on a charged particle is perpendicular to its velocity. Hence there will not any change in its speed or kinetic energy.
The magnetic force will deflect the particle without changing speed and in a uniform field, the particle will move along a circle perpendicular to the magnetic field. The conclusion is that, the magnetic force provides centripetal force. If r be the radius of the circle, then = ²/
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(LHS is the expression for magnetic force and RHS is expression mass × acceleration) = /
The time taken to complete the circle is = 2/ = 2/
The time period or time taken to complete one circle is independent of speed. But the radius depends on . Hence if speed increases, the radius is larger. Frequency of revolutions is
= 1/ = /2
This frequency is called cyclotron frequency. •
If the velocity of charge is not perpendicular p erpendicular to the magnetic field, the resultant path will be a helix. The radius of the path will be determined by velocity component which is perpendicular to the magnetic field. If is the angle between and , then there are two components of velocities velocities
(i) (ii)
sin perpendicular to magnetic field B this component provides circular motion about B cos parallel to the magnetic field B this component component provides motion of translation ( sin )2
= sin
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or
=
sin
to complete one revolution is =
2 sin
=
2
T is independent of , . 2 Pitch = cos . = cos . ∴ or
Pitch
= cos .
2 sin
= 2 cot
In a current carrying wire, electrons, which are charge carrying particles are moving and hence in a magnetic field, a current carrying conductor wo uld experience magnetic force. If a straight wire of length carrying a current is placed in a uniform magnetic field B, then the force on it is � ⃗ = ⃗ ×
The quantity denotes current element of length of . If there is a rectangular loop carrying current in a uniform magnetic field B then net torque acting on the loop is Г = sin
Where, = current in the loop = area
B = magnetic field = the angle of inclination of the loop with the plane perpendicular to the plane of magnetic field.
We can also define � = ⃗ × � Г can be termed as the magnetic dipole moment or simply magnetic moment of the current loop. If there are turns in the loop, each turn experiences a torque.
The net torque is � = ⃗ × � Г ⃗ = ⃗
field.
� and electric field � experiences a force A moving charge in presence of a magnetic field � ⃗ = ⃗ + ⃗ = � + ⃗ × �) ⇒ ⃗ = (� +⃗ × � and ⃗ = −⃗ and resultant field is called crossed If is zero then � should be ⊥ to
� all the three are collinear: When ⃗ , � and In this situation as the particle is moving parallel or anti parallel to the field (i.e., = 0 ͦ or 180 ͦ), the magnetic force on it will be zero and only electric force will act and so = =
Hence the particle will pass through the field following a straight line path with change in speed.
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� are mutually perpendicular: When ⃗ , � and � are such that In this situation if � and
i.e.,., = ⃗ = ⃗ + ⃗ = 0 i.e
= 0 or cross field
�. The particle will move undeflected perpendicular to � and
