At a certain distance from a point charge, the potential due to the charge is �|5.93 V, and the magnitude of the electric field is 13.5 V/m. (Take the potential to be zero at infinity.) Is the electric field directed toward or away from the charge?
Here is my attempt. Since potential due to charge is -, work done must be -. Therefore the electric field must be directed away from the charge. Is this correct???
YEs.
Your understanding is partly correct, but let me clarify the concept further.
In electrostatics, the electric field and the potential have a relationship described by the equation:
E = -∇V
where E is the electric field, V is the electric potential, and ∇ represents the gradient operator. The negative sign indicates that the electric field points in the direction of decreasing potential.
Given that the potential due to the charge is -5.93 V, we can conclude that the electric field at that location points in a direction opposite to the direction of increasing potential.
However, it's important to note that the magnitude of the electric field alone cannot determine the direction. In this case, since the potential is decreasing, the electric field would be directed towards the charge, not away from it.
So, to answer your question, the electric field is directed towards the point charge.