MAGNETIC FIELD :
In electronics, we have studied that a static charge produces an electric field. The electric field is a region of space around a static charge in which its electric effect can be felt. The electric field at a particular point can is due to one or more charges. If there are more charges, the field adds vectorially, using the principle of superposition. Once the effective electric field E at a point is known, the force on a test charge qο at that point can be given by
F = qο E
Just as a static charge produces an electric field, a moving charge or current through the conductor produces a magnetic field.
The magnetic field is a space around a conductor carrying current or magnet in which its magnetic effect can be felt.
The magnetic field disappears as soon as the current is switched off or charges stop moving. It means a moving charge is both a source of the electric field and a magnetic field. The magnetic field denoted by B is a vector. It is a called magnetic induction or magnetic flux density. It has several basic properties identical to the electric field. The effective magnetic field B at a point due to the magnetic field of several sources is the vector addition of the magnetic field of each source at that point, i.e.,
B = B1 + B2 + B3 + ....
where B1, B2, B3 ... are the magnetic field at a point due to individual sources of the magnetic field. It means the magnetic field obeys the superposition principle.
To define the magnetic field B, we deduce an expression for the force on a moving charge in a magnetic field.
Consider a positive charge q moving in a uniform magnetic field B, with a velocity v. Let the angle between v and B be θ. Due to interaction between the magnetic field produces due to moving charge (i.e., current) and magnetic field applied, the charge q then experiences a force, which depends on the factors given below :
(i) The magnitude of the force F experienced by the moving charge is directly proportional to the magnitude of the charge i.e.
F ∝ q
(ii) The magnitude of the force F is directly proportional to the component of velocity acting perpendicular to the direction of the magnetic field, i.e., F ∝ sin θ
(iii) The magnitude of the force F is directly proportional to the magnitude of the magnetic field applied, i.e., F ∝ B
combining the above factors, we get
F ∝ q v sin θ B or F = kqv B sin θ
where k is a constant of proportionality. Its value is found to be one, i.e., k=1.
∴ F = qv B sin θ
Direction of F
F in the direction of cross-product of velocity v and magnetic field B, perpendicular to the plane containing v and B. It is directed as given by the Right-Hand-Screw Rule or Right-hand Rule.
If v and B are in the plane of the paper, then according to Right-Hand Rule, the direction of F on the positively charged particle will be perpendicular to the plane of paper upward, and on the negatively charged particle will be perpendicular to the plane of paper downward.
Direction of B
If v = 1 , q = 1 and sin θ = 90ο , then F = 1 x 1 x B x 1 =B.
Thus the magnetic field induction at a point in the field is equal to the force experienced by a unit charge moving with a unit velocity perpendicular to the direction of magnetic field at that point.
Special cases.
Case(i) If θ = 0ο or 180ο , then sin θ = 0.
∴From, F = qv B(0) = 0.
It means a charged particle moving parallel to the direction of the magnetic field does not experience any force.
Case(ii) If v = 0, then, F = qv B sin θ = 0.
It means, If a charged particle is at rest in a magnetic field, it experiences no force.
Case(iii) If θ = 90ο , then sin θ = 1
∴ F = qv B(1) = qv B(Maximum).
It means, If a charged particle is moving along a line perpendicular to the direction of the magnetic field, it experiences a maximum force. The direction of this force can also be determined by Fleming's Left-Hand Rule, which can be stated as follows :
If we stretch the first finger, the central finger and the thumb of left hand mutually perpendicular to eachother such that the first finger points to the direction of magnetic field, the central finger points to the direction of electric current (motion of the positive charge) then the thumb represents the direction of force experienced by the charged particle.
You must be logged in to post a comment.