Magnetic field of a moving charge

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SUMMARY

The discussion centers on calculating the magnetic field produced by a moving negative charge, specifically q = −3.20×10-6C, at a given point in space. The velocity of the charge is υ⃗ =(7.50×104m/s)ι^+((−4.90)×104m/s)j^, and the magnetic field is determined using the equation B = μ0/4π * (q(v × r))/r2. Participants emphasize the necessity of using vector operations, particularly the cross product, to accurately compute the magnetic field components rather than treating them independently.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically the Biot-Savart Law.
  • Familiarity with vector mathematics, including cross products.
  • Knowledge of the magnetic constant (μ0) and its application in magnetic field calculations.
  • Basic principles of charge motion and its effects on magnetic fields.
NEXT STEPS
  • Study the Biot-Savart Law in detail to understand magnetic field generation by moving charges.
  • Learn how to compute cross products of vectors in three-dimensional space.
  • Explore the implications of charge velocity on magnetic field strength and direction.
  • Practice solving similar problems involving magnetic fields from multiple moving charges.
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Students and professionals in physics, particularly those focusing on electromagnetism, as well as educators seeking to enhance their understanding of magnetic fields generated by moving charges.

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Homework Statement


A negative charge q = −3.20×10-6C is located at the origin and has velocity υ⃗ =(7.50×104m/s)ι^+((−4.90)×104m/s)j^.
At this instant what is the magnetic field produced by this charge at the point x = 0.230 m , y = -0.300 m , z= 0? Give the x, y and x components

Homework Equations


B = u0/4π. (qv x r)/r2

The Attempt at a Solution


So to find Bx I've tried using r = 0.230 and v = 7.5x104 giving 10-7 x 3.2 x 10-6 x 7.5 x 104/0.2302. However i have a feeling I can't just take the x/y components individually. I know that a cross product goes to 1 if the components are perpendicular and 0 if they are parallel and feel like this will help but i just can't put it all together to give me the correct answer. any hints would be very much appreciated!
 
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You are correct - you cannot just take the components individually like that. You have a vector equation, why not use it?
Do you know how to evaluate a cross product between two arbitrary vectors?
 

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