Derive an expression for the force experienced by a current carrying straight conductor placed in amagnetic field. under what condition , is the force is (a) zero and (b) maximum ?
Hello,
Solution
When the direction of current is at right angle to the direction of magnetic field, the force is maximum.
Let us consider a Current Carrying conductor of length L placed in a magnetic field B .It is represented by X.
Let the field be confined to Length L.So only the part of wire of length L is inside the Magnetic field.
magnetic force on a single charge is given by:
F=qvB
let total charge inside the Magnetic field be Q so magnetic force on current carrying conductor is given by
F=QVB-----------1
the time taken by the charge q to cross the field is
t=L/V
v=L/t------------2
substituting this in equation 1 we get
F=Q(L/t)B
F=(Q/t) LB
but Q/T is electric current So F=ILB
This equation hold good when direction of electric current is perpendicular of magnetic field.
if at an angle then
F=ILBsinθ
We can use right hand rule to find out the direction of force on the current carrying wire. or Fleming's Left hand rule can also be used.
F will be maximum when I and B are perpendicular
F will be minimum when θ=0°
Hope it helps
