Comparison of Electric and Magnetic Forces

In summary, when comparing the electric and magnetic forces between two positive point charges with parallel instantaneous velocities, the ratio of the magnetic force to the electric force is given by Fmag/Felec = v1*v2/c^2, where v1 and v2 are the velocities of the particles and c is the speed of light. To solve this problem, one can use the Lorentz force and the Biot-Savart law to determine the magnetic field caused by the first particle and then find the magnetic force on the second particle as it moves through the magnetic field. Finally, the speed of light can be incorporated into the solution through the relation c = 1/\sqrt{\mu _0 \epsilon _0}.
  • #1
godiva
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Homework Statement


Suppose that the instantaneous velocities of two positive point charges are parallel. Compare the electric and magnetic forces. Show that the ratio of the magnetic force (Fmag) to the electric force (Felec) is: Fmag/Felec = v1*v2/c^2
Where v1 and v2 are the velocities of particle 1 and particle 2 respectively, and c is the speed of light.

Homework Equations


F = qE + qv*B

The Attempt at a Solution


I know that you need to use the Lorentz force in some form, but I am confused as to how the speed of light is incorporated into the solution. This is a practice problem for my exam later on this week, so any help would be appreciated.
 
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  • #2
Hello godiva,

Welcome to Physics Forums!
godiva said:
I know that you need to use the Lorentz force in some form, but I am confused as to how the speed of light is incorporated into the solution. This is a practice problem for my exam later on this week, so any help would be appreciated.
The easy way is to first figure out what the magnetic field B is, caused by the first moving particle (charge q moving at a speed of v1). Use the Biot-Savart law for a single particle. If you are using the general Biot-Savart law that is a function of current and wire length, substitute (current times length of wire) with (charge of particle times velocity of particle), which is the same thing for a single particle.

Once you know the magnetic field caused by the first particle, find the magnetic force on the second particle as it moves through the magnetic field with a velocity v2.

Then take the ratio of magnetic force to the electric force.

Finally, note that [itex] c = 1/\sqrt{\mu _0 \epsilon _0} [/itex]
 
Last edited:

1. What is the difference between electric and magnetic forces?

Electric forces are caused by the interaction between charged particles, while magnetic forces are caused by the interaction between moving charged particles. Electric forces can act on both stationary and moving charges, while magnetic forces only act on moving charges.

2. How are electric and magnetic forces similar?

Both electric and magnetic forces are types of electromagnetic forces. They both follow the inverse square law, meaning that the strength of the force decreases with distance. Both electric and magnetic forces can also be attractive or repulsive depending on the charges involved.

3. How do electric and magnetic forces affect charged particles?

Electric forces cause charged particles to either attract or repel each other, depending on their charges. Magnetic forces cause charged particles to move in a circular or spiral path, known as a magnetic field, when they are in the presence of a magnetic field.

4. Can electric and magnetic forces be separated?

No, electric and magnetic forces are two aspects of the same fundamental force, known as the electromagnetic force. They cannot be separated and are always present together.

5. How do electric and magnetic forces play a role in everyday life?

Electric and magnetic forces are essential for many technologies that we use in our daily lives. Electric motors, generators, and transformers all rely on the interaction between electric and magnetic fields. They also play a crucial role in the functioning of electronic devices, such as computers and televisions.

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