Magnetic Field of a Moving Point charge

In summary, the problem involves a point charge of q1=3.6nC moving at a speed of 4.5 x 107m/s in the +y direction along the line x=3m. The magnetic field produced by this charge at the origin when it is at the point x=3m, y=4m is approximately 0.39nT in the +z direction. This is calculated using the Biot Savart Law, where the direction of r is from the charge to the point where B is being calculated.
  • #1
OmegaFury
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Homework Statement


A point charge of q1=3.6nC is moving with speed 4.5 x 107m/s parallel to the y-axis along the line x=3m. The magnetic field produced by this charge at the origin when it is at the point x=3m, y=4m is approximately:

Homework Equations


vector B= (magnetic constant/4pi) (q(vector v X unit vector r)/r2)
magnetic constant= 4pi x 10-7 (Tesla x meter)/Ampere

The Attempt at a Solution


The problem here is a curious cross product outcome.
vector v= 4.5 x 107j = <0, 4.5 x 107, 0>
vector r= <3-0, 4-0, 0-0>= <3,4,0>
magnitude of r= sqrt(32+42)= 5
unit vector r= vector r/ magnitude of vector r= <3,4,0>/5

[itex]\vec{v}[/itex]X[itex]\hat{r}[/itex]= <0, 4.5 x 107, 0> X <3, 4, 0> =

((4.5 x 107(0) - 0(4))i - (0(0) - 0(3))j + (0(4) - 4.5 x 107(3))k)/5 =

(-13.5 x 107j)/5= <0, 0, -13.5 x 107>/5

Wouldn't that imply that the cross product vector is in the -Z direction? However, using right hand rules, shouldn't the cross product vector be in the positive Z direction?
 

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  • #2
Welcome to PF.

In the Biot Savart Law, the direction of r is from the current element or charge to the point where B is being calculated. So r is <-3,-4,0> in this case.

p.s. I presume the charge is moving in the +y direction?
 
  • #3
Redbelly98 said:
Welcome to PF.

In the Biot Savart Law, the direction of r is from the current element or charge to the point where B is being calculated. So r is <-3,-4,0> in this case.
Ahhhhh. So I had it reversed.
Redbelly98 said:
p.s. I presume the charge is moving in the +y direction?
Yes, the charge is moving in the +y direction.

So the cross product would now be: <0, 4.5 x 107, 0>m/s X <-3, -4, 0>/5 =
(0--(3/5)(4.5 x 107)) k= +2.7 x 107m/s k

Then vector B= (magnetic constant/ 4pi) (3.6 x 10-9C)(2.7 x 107m/s k) / (25m2)= 3.89 x 10-10 T k. Which is equal to 0.39nT k

Thank you for your assistance :)
 
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FAQ: Magnetic Field of a Moving Point charge

What is a magnetic field?

A magnetic field is a region where a magnetic force can be detected. It is created by moving electric charges and can influence the motion of other electrically charged objects.

How is a magnetic field created by a moving point charge?

According to the right-hand rule, when a point charge moves, it creates a magnetic field that is perpendicular to both the direction of the charge's movement and the direction of the force acting on the charge. This magnetic field is circular in shape and decreases in strength as the distance from the point charge increases.

What factors affect the strength of a magnetic field created by a moving point charge?

The strength of the magnetic field created by a moving point charge is affected by the speed of the charge, the distance from the charge, and the charge's electric field strength. Additionally, the strength of the magnetic field is inversely proportional to the square of the distance from the charge.

How can the direction of a magnetic field created by a moving point charge be determined?

The direction of the magnetic field can be determined using the right-hand rule. If the thumb of the right hand points in the direction of the charge's movement and the fingers curl in the direction of the force acting on the charge, then the direction of the magnetic field will be perpendicular to both the thumb and fingers.

What are some real-world applications of magnetic fields created by moving point charges?

Magnetic fields created by moving point charges have many practical applications, including in electric motors, generators, and particle accelerators. They are also used in magnetic resonance imaging (MRI) machines and in the production of electricity from renewable sources such as wind and hydro power.

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