What Determines the Acceleration of a Charge in an Electric Field?

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SUMMARY

The acceleration of a positive charge q in an electric field created by two other charges, Q1 and Q2, is determined by the magnitudes and signs of these charges. Specifically, the acceleration is directed towards the charge of greater magnitude, or towards the positive charge when Q1 and Q2 are of opposite signs. The overall direction of acceleration is dictated by the vector sum of the electric fields produced by Q1 and Q2. This understanding is crucial for solving problems involving electric forces and fields in electrostatics.

PREREQUISITES
  • Understanding of Coulomb's Law
  • Familiarity with electric fields and forces
  • Knowledge of vector addition
  • Basic concepts of charge interactions
NEXT STEPS
  • Study the principles of Coulomb's Law in detail
  • Learn about vector addition in the context of electric fields
  • Explore the concept of superposition of electric fields
  • Investigate the behavior of charges in different configurations, such as triangular arrangements
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Students studying electrostatics, physics educators, and anyone interested in understanding the dynamics of charged particles in electric fields.

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Homework Statement


When a positive charge q is placed in the field created by two other charges Q1 and Q2, each a distance r away from q, the acceleration of q is
a. in the direction of the charge Q1 or Q2 of smaller magnitude.

b. in the direction of the charge Q1 or Q2 of greater magnitude.

c. in the direction of the negative charge if Q1 and Q2 are of opposite sign.

d. in the direction of the positive charge if Q1 and Q2 are of opposite sign.

e. in a direction determined by the vector sum of the electric fields of Q1 and Q2.

The Attempt at a Solution

 
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I'm guessing that you are not supposed to assume that q is on a line connecting the other two charges. In other words, I'm guessing that you are supposed to assume that the charges are put on the corners of some sort of an isosceles triangle (conceptually).

(Otherwise you could come up with certain special cases where each choice would be true, even through it wouldn't be true in general.)
 
Try to come up with a counterexample for which (c) is false - that is, can you find some situation in which Q1 and Q2 have opposite sign, and the acceleration of q is away from the negative charge? (Hint: it can be done with all the particles on a line)
 

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