Electric current is charges in motion. We know that each charge
experiences a magnetic force. Thus the current carrying wire (constituting collection of charges in motion) experiences magnetic force when it is kept in a magnetic field.
• Can you determine the magnetic force on a current carrying wire which is placed along a magnetic field?
We know that each charge experiences no magnetic force because they are moving parallel to the direction of field along the field. So the force acting on wire is zero when it is kept along a magnetic field.
Let us find the magnetic force on a straight wire carrying current which is kept perpendicular to a uniform magnetic field ‘B’. This ‘B’ is directed into the page. It is represented by ‘x’ as shown in the figure 9. Let the field be confined to the length L. So only the part of the wire of the length ‘L’ is inside the magnetic field. Remaining wire is outside the magnetic field. We know that the electric current means charges in motion hence they move with a certain velocity called drift velocity ‘v
The magnetic force on a single charge is given by,
F0 = q v B
Let total charge inside the magnetic field be Q. So magnetic force on the current carrying wire is given by
F = Q v B ..................(1)
The time taken by the charge (Q) to cross the field be t = L/ v→ v =L/ t ..................(2)
substituting this in equation 1, we get,
F=QLB /t → F =Q/ t LB ..................(3)
We know that Q/t is equal to the electric current in the wire,
t=Q/t
Substituting ‘I’ in the equation 3, we get
F = ILB.................(4)
Note:
This equation holds well only when direction of electric current is perpendicular to magnetic field.
In fig.-9, you can observe the bending in the wire due to the force applied on it.
• What is the force on the wire if its length makes an angle ‘θ’ with the
magnetic field?