Magnitude of a magnetic field a a point

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SUMMARY

The discussion focuses on calculating the magnetic field at point P due to a moving point charge Q on the x-axis. The magnetic field produced at point P when the charge is at the origin is -0.8 μT in the k^ direction. The correct formula for the magnetic field is given as B = (μ₀/4π) * Q * (v × r̂) / r², where v is the velocity of the charge and r̂ is the unit vector from the charge to point P. The participants emphasize the importance of correctly applying the cross product between the velocity vector and the unit vector to derive the magnetic field at the new position of the charge.

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  • Understanding of the Biot-Savart Law for magnetic fields
  • Familiarity with vector cross products
  • Knowledge of unit vectors and their application in physics
  • Basic principles of electromagnetism, specifically regarding moving charges
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  • Study the Biot-Savart Law in detail to understand magnetic field calculations
  • Learn about vector cross products and their geometric interpretations
  • Explore examples of magnetic fields produced by moving charges
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Jstuff
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A point charge Q moves on the x-axis in the positive direction with a speed of 450 m/s. A point P is on the y-axis at y = +70 mm. The magnetic field produced at point P, as the charge moves through the origin, is equal to -0.8 μT k^. When the charge is at x = +40 mm, what is the magnitude of the magnetic field at point P? (μ0 = 4π × 10-7 T · m/A)

Hey guys so I am having trouble understanding this problem. Well I actually understand the problem, but I am having trouble applying the formulas.

I understand that to do that problem I need to use the formula for the magnetic field created by a moving point charge. B=(μ_0 q r x v)/(4π r^2) to solve for the charge.
I did this for position one where the degree between the angle will be sin(90)=1 and got -.00124C.
I then applied the equation again to solve for the magnetic field at the new position. My trouble I am having is the cross product between r and v at this locations. I put r into unit vector form and crossed it with v in the positive x direction, but I do not get the right answer.
 
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Jstuff said:
A point charge Q moves on the x-axis in the positive direction with a speed of 450 m/s. A point P is on the y-axis at y = +70 mm. The magnetic field produced at point P, as the charge moves through the origin, is equal to -0.8 μT k^. When the charge is at x = +40 mm, what is the magnitude of the magnetic field at point P? (μ0 = 4π × 10-7 T · m/A)

Hey guys so I am having trouble understanding this problem. Well I actually understand the problem, but I am having trouble applying the formulas.

I understand that to do that problem I need to use the formula for the magnetic field created by a moving point charge. B=(μ_0 q r x v)/(4π r^2) to solve for the charge.

The formula for B is not correct. It should be \vec B = \frac {\mu_0}{4\pi} Q \frac{\vec v\times\hat r}{r^2}
so you have to cross the velocity with the unit vector pointing from the charge to P.
ehild
 
ehild said:
The formula for B is not correct. It should be \vec B = \frac {\mu_0}{4\pi} Q \frac{\vec v\times\hat r}{r^2}
so you have to cross the velocity with the unit vector pointing from the charge to P.
ehild
Okay, so then I am crossing (450i) x (.O4i-.07j)1/.08. Correct?
 
If 0.08 in the denominator stands for ##\sqrt{65}## then it is approximately correct.
 

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