Finding the magnitude of the magnetic field of a moving point charge

In summary: Thanks for getting back to me.In summary, the magnetic field at a location given by vector r from the moving point charge is: 0 when t=0.1μs.
  • #1
OmegaFury
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Question: A point charge is moving with speed 2 x 107m/s along the x axis. At t=0, the charge is at x= 0m and the magnitude of the field at x=4m is B0. The magnitude of the magnetic field at x= 4m when t= 0.1μs is:The equation and my attempt at solving it is in the attachment.
--I also converted amperes to 1C/1s and I figured that theta is 90 degrees and the magnitude of the unit vector r is one, and thus the cross product of vector v and unit vector r is 2 x 10^7 m/s. ( 2 x 10^7 times one times sin(90 degrees).
 

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  • #2
OmegaFury said:
Question: A point charge is moving with speed 2 x 107m/s along the x axis. At t=0, the charge is at x= 0m and the magnitude of the field at x=4m is B0. The magnitude of the magnetic field at x= 4m when t= 0.1μs is:


The equation and my attempt at solving it is in the attachment.
--I also converted amperes to 1C/1s and I figured that theta is 90 degrees and the magnitude of the unit vector r is one, and thus the cross product of vector v and unit vector r is 2 x 10^7 m/s. ( 2 x 10^7 times one times sin(90 degrees).

Your equation for the magnetic field at a location given by vector r from the moving point charge is:
$$\vec{B} = \frac{\mu_o}{4\pi}q\frac{\vec{v}\times \vec{r}}{r^2}$$
You weren't given a value for the point charge q (so your use of the elementary charge is not warranted).

The problem seems to indicate that the "test location" where the field is to be evaluated is directly along the path of the moving charge (the charge is moving along the x-axis, the test location is at x=4m and no y-offset is given). What should that tell you about the results of the cross product v x r ?
 
  • #3
gneill said:
The problem seems to indicate that the "test location" where the field is to be evaluated is directly along the path of the moving charge (the charge is moving along the x-axis, the test location is at x=4m and no y-offset is given).What should that tell you about the results of the cross product v x r ?

That would make the cross product zero, wouldn't it? But that would make the magnetic field zero. If that's true, why would it change when t= 0.1 microseconds?
 
  • #4
OmegaFury said:
That would make the cross product zero, wouldn't it? But that would make the magnetic field zero. If that's true, why would it change when t= 0.1 microseconds?

Good question :smile: It wouldn't change. Is the problem statement exactly as you've given it?
 
  • #5
Exactly as given. It should be 0 though at any given time if vector v is on the same axis as vector r. Thanks for pointing that out. There might be a typo in the problem or something. If, perhaps, the field point was on a different axis or the charge was moving along a different axis, then the magnetic field would change over time because the cross product wouldn't be 0, and the distance r to the field point would be changing with time.
 
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  • #6
OmegaFury said:
Exactly as given. It should be 0 though at any given time if vector v is on the same axis as vector r. Thanks for pointing that out. There might be a typo in the problem or something. If, perhaps, the field point was on a different axis or the charge was moving along a different axis, then the magnetic field would change over time because the cross product wouldn't be 0, and the distance r to the field point would be changing with time.

Yup. That's my take on it too.
 

FAQ: Finding the magnitude of the magnetic field of a moving point charge

1. What is the formula for finding the magnitude of the magnetic field of a moving point charge?

The formula for finding the magnitude of the magnetic field of a moving point charge is given by B = (μ0/4π) * (q * v * sinθ)/r^2, where B is the magnetic field, μ0 is the permeability of free space, q is the charge of the moving point charge, v is the velocity of the charge, θ is the angle between the velocity and the direction of the magnetic field, and r is the distance between the charge and the point where the magnetic field is being measured.

2. How does the velocity of the moving point charge affect the magnitude of the magnetic field?

The velocity of the moving point charge directly affects the magnitude of the magnetic field. As the velocity increases, the magnitude of the magnetic field also increases. This is because the magnetic field is directly proportional to the velocity of the charge.

3. What is the role of the angle between the velocity of the charge and the direction of the magnetic field?

The angle between the velocity of the charge and the direction of the magnetic field, also known as the angle of deflection, affects the magnitude of the magnetic field. The magnetic field is strongest when the angle is 90 degrees, and it becomes weaker as the angle decreases or increases.

4. How does the distance between the charge and the point where the magnetic field is being measured affect the magnitude of the magnetic field?

The distance between the charge and the point where the magnetic field is being measured, also known as the separation distance, has an inverse relationship with the magnitude of the magnetic field. As the distance increases, the magnetic field becomes weaker, and as the distance decreases, the magnetic field becomes stronger.

5. What is the significance of the permeability of free space in calculating the magnitude of the magnetic field?

The permeability of free space, denoted by μ0, is a constant that represents the ability of a vacuum to support the formation of magnetic fields. It plays a crucial role in calculating the magnitude of the magnetic field and is used as a conversion factor in the formula. Without taking into account the permeability of free space, the calculated value of the magnetic field would not be accurate.

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