Why is the electric field a vector quantity while the electric potential is a scalar?
The correct answer and explanation is :
Correct Answer:
The electric field is a vector quantity because it has both magnitude and direction, representing the force per unit charge at a point in space. The electric potential is a scalar quantity because it represents the electric potential energy per unit charge and has only magnitude, not direction.
Explanation (300 words):
Electric field and electric potential are two fundamental concepts in electromagnetism, but they differ significantly in nature and how they describe the influence of electric charges.
The electric field (E) is a vector quantity because it describes the force that a positive test charge would experience at a particular point in space. Force, by definition, is a vector—it has both magnitude and direction. The direction of the electric field is the direction of the force on a positive charge. For example, near a positive point charge, the electric field points away from the charge, while near a negative charge, it points toward the charge. Since force and displacement are both vectors, the electric field must also be a vector to correctly represent the physics involved.
On the other hand, the electric potential (V) is a scalar quantity. It represents the amount of potential energy per unit charge at a point, not the direction in which that energy would cause a charge to move. Electric potential is related to work done by or against the electric field, and work is a scalar—it only measures the energy transferred, regardless of the path taken or direction. Since electric potential involves no direction, just a value, it is expressed as a scalar.
Mathematically, the electric field is the negative gradient of the electric potential:
$$
\vec{E} = -\nabla V
$$
This equation shows that while the potential is scalar, its rate of change in space (gradient) gives rise to the vector field, the electric field. This distinction is key in understanding electric interactions in physics and engineering.