Name: Magnetic Induction
Uploaded: 2019-07-19
Duration: 4 min 29 s
Description: Are you aware that you can magnetise a material just by bringing it close to a magnet? Let’s explore the principle of magnetism in this video.

Question

Deduce an expression for the force on a current carrying conductor placed in a magnetic field.

Accepted Answer

Force on a current-carrying conductor placed in a magnetic field: Let us consider a conductor PQ of length l and area of cross-section A. The conductor is placed in a uniform magnetic field of induction B making an angle θ with the field (figure). A current I flows along PQ. Hence, the electrons are drifted along QP with drift velocity vd. If n is the number of free electrons per unit volume in the conductor, then the current is
$I = n A v_{d} e$
Multiplying both sides by the length of the conductor,
$∴ I l = n A v_{d} e l$
Therefore the current element,
$I l = - n A \vec{v_{d}} e l . . . . (1)$
The negative sign in the equation indicates that the direction of current is opposite to the direction of drift velocity of the electrons. Since the electrons move under the influence of magnetic field, the magnetic Lorentz force on a moving electron.
$\vec{f} = e (\vec{v_{d}} \times \vec{B}) . . . . (2)$
The negative sign indicates that the charge of the electron is negative.
The number of free electrons in the conductor
N=nAl......(3)
The magnetic lorentz force on all the moving free electrons
$\vec{F} = \vec{N} f ,$
Substituting equations (2) and (3) in the above equation
$F = n A l - e (v \times b) \Rightarrow F = - n A l e v \times B . . . . (4)$
Substituting equation (1) in equation (4)
F=Il×B
This total force on all the moving free electrons is the force on the current t carrying conductor placed in the magnetic field.
Magnitude of the force: The magnitude of the force is F=BIl sinθ
(i) If the conductor is placed along the direction of the magnetic field, $θ = 0^{\circ}$ , therefore force F=0.
(ii) If the conductor is placed perpendicular to the magnetic field, $θ = 90^{\circ}$ ,F=BIl. Therefore the conductor experiences maximum force.

Deduce an expression for the force on a current carrying conductor placed in a magnetic field.

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