Calculating Electric Field at 4th Corner of Rectangle with 3 Charges

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SUMMARY

The calculation of the electric field at the fourth corner of a rectangle with three positive charges (q1, q2, and q3) involves determining the vector sum of the electric fields produced by each charge. The electric field due to a charge is calculated using the formula E = q/(4πε₀r²), where r is the distance from the charge to the point of interest. The components of the electric field are then resolved into x and y directions using trigonometric functions, and the resultant electric field is found by summing these components and applying the Pythagorean theorem. This method confirms the correct approach to solving the problem.

PREREQUISITES
  • Understanding of Coulomb's Law and electric fields
  • Familiarity with vector addition and trigonometry
  • Knowledge of the concept of electric field strength
  • Basic understanding of geometry related to rectangles
NEXT STEPS
  • Study the principles of vector addition in physics
  • Learn about electric field calculations for multiple point charges
  • Explore trigonometric functions and their applications in physics
  • Investigate the concept of superposition in electric fields
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Students and professionals in physics, electrical engineering, and anyone interested in understanding electric fields and charge interactions in geometrical configurations.

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I have this question:

Positive charges are situated at 3 corners of a rectangle with charges q1, q2, and q3. Given each of their distances from the 4th corner of the rectangle, what is the electric field at the 4th corner?

Would it be the vector sum of the electric field of each of those at the 4th corner?
So, for q1, say it's r meters away, the field at that point would be:
E = q1/(4pi epsilon0 times r^2) ...
And then, knowing the angle at which it's pointed (relative to, say, the horizontal) I'd multiply it by the cosine of that angle and sine to end up with the x and y components, rinse and repeat for all of the others, add them all up (considering directions and signs) and then use Pythagoras' theorem, then finding the direction? Or am I thinking wrong?
Just want to know if I'm thinking of the right idea!
Thanks!
 
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