obtain an expression for force experienced by a conductor carrying current placed in an external magnetic field.
Answers
Given: Current carrying wire with a given length placed in an external magnetic field
To find: Expression for force acting on it
solution:
force experienced by a conductor carrying current placed in an external magnetic field will be
F=ILBsinθ
Let L= length of the metallic conductor
A= cross sectional area
B= uniform magnetic field
θ = angle made by length of the conductor with the direction of magnetic field B
I = current in the conductor
According to free electron model
I= neAVd
where n is no. of free electrons and Vd id drift velocity
Magnetic force on each electron will be eVdBsinθ
Number of electrons in the conductor will be nAL
Net magnetic force on each conductor
F= ( force on one electron) × ( number of electrons)
F= (eVdBsinθ)× (nAL)
F= (neAVd ).BLsinθ
F=ILBsinθ
Therefore the general formula for the force acting on a current carrying conductor is F=ILBsinθ