Is electric field radially inwards or outwards

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SUMMARY

The direction of an electric field, denoted as ##\vec E##, is determined by the rate of change of electric potential (V) with respect to distance (r). Specifically, ##\vec E## points outwards when the electric potential decreases with increasing distance (dV/dr < 0) and inwards when the potential increases (dV/dr > 0). The force on a positively charged test particle aligns with the electric field direction, while the force on a negatively charged particle opposes it. Understanding the relationship between electric field and potential is crucial, as expressed by the equation E = -∇V.

PREREQUISITES
  • Understanding of electric potential (V) and its mathematical representation.
  • Familiarity with vector calculus, specifically gradients (∇).
  • Knowledge of charge interactions, particularly with positively and negatively charged particles.
  • Basic comprehension of electric field notation and symbols used in physics.
NEXT STEPS
  • Study the mathematical implications of the equation E = -∇V in various contexts.
  • Learn about electric field visualization techniques and their applications in physics.
  • Explore the relationship between electric fields and forces on charged particles in different scenarios.
  • Investigate the implications of electric field direction in circuit design and electromagnetic theory.
USEFUL FOR

This discussion is beneficial for physics students, educators, and professionals in electrical engineering who seek to deepen their understanding of electric fields and potentials.

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In general, ##\vec E## points in the direction that V decreases most rapidly.

In this case, V depends only on r, so ##\vec E## points outwards if V decreases with increasing r (i.e. dV/dr < 0), and inwards if V increases with increasing r (dV/dr > 0).
 
The force on a positively charged test particle is in the direction of the electric field; the force on a negatively charged test particle is opposite to the direction of the electric field. If you're careful with your signs, you'll get the right answer just from doing the calculation because you'll write a negative charge as ##-Q## and the negative sign carries through into the sign of the force - but wise people also take a moment to visualize the setup and make sure that their answer has the force pointing in a sensible direction.
 
Alright man so what the symbols mean are: if it is the "x" symbol it means the field is going into the page (away from you) and if it is the other symbol then it means the field is coming out of the page (at you)
 
Sorthal said:
Alright man so what the symbols mean are: if it is the "x" symbol it means the field is going into the page (away from you) and if it is the other symbol then it means the field is coming out of the page (at you)

It is better to describe the Field in terms of the Potential - that avoids having to think of a 'page' or where you (or I) happen to be standing. Basically:
E = -∇V or the gradient of the Potential. It's the way that a positively charged 'ball' would 'roll', as jibell was hinting.
 

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