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In addition to the revision notes for Magnetic Force on a Wire Moving Inside a Magnetic Field. Lorentz Force on this page, you can also access the following Magnetism learning resources for Magnetic Force on a Wire Moving Inside a Magnetic Field. Lorentz Force
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 16.4 | Magnetic Force on a Wire Moving Inside a Magnetic Field. Lorentz Force |
In these revision notes for Magnetic Force on a Wire Moving Inside a Magnetic Field. Lorentz Force, we cover the following key points:
The magnetic force F1 acting on each charge due to their directed motion in the conducting wire is calculated by dividing the total magnetic force Ftot by the number of charges n flowing in the entire length L of the wire. Mathematically, we have:
Giving that the current I is
where ΔQ is the charge flowing through the wire in the time interval Δt and
where v is the velocity of moving charges throughout the wire during this interval, we obtain for the magnetic force acting on an elementary charge in motion
where
The vector form of the above equation is
and the direction of magnetic force is found by using the Fleming's Left Hand Rule.
Not always the direction of particles motion is perpendicular to the magnetic field lines. When these two vectors form another angle θ to each other, we have to consider this angle as well. The formula of magnetic force for an elementary electric charge in such conditions therefore becomes
However, the force vector will still be perpendicular to the plane of the other two vectors (v and B).
We can use the same approach for larger charged objects as well. In this case, we apply the vector equation
or its scalar equivalent
to calculate the magnetic force of a charged object in motion. This force is the same force we have called earlier as "the Ampere's force".
Any particle placed inside a uniform magnetic field will move in uniform circular motion, where the magnetic force will act as a centripetal force. The radius of the resulting curved path is obtained by analyzing the magnetic-centripetal force equivalence, i.e.
The period of rotation for a particle in circular motion inside a uniform magnetic field is:
or
The total force produced on a charged object due to the existence of the two fields - electric and magnetic - is the sum of the corresponding forces. This overall effect is known as the Lorentz Force and its vector form is
or
The electric force is easier to find as it is always in the direction of electric field (when it is produced by a positive charge). As for the magnetic force, its direction is found using the Fleming's Left Hand rule.
Lorentz Force is a demonstration of the fact that electricity and magnetism cannot exist without each other. Lorentz Force exists only when charges are in motion. Stationary charges produce only an electric effect, not a magnetic one.
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