Which relation defines the electric field?

Which relation defines the electric field?

• A. E = F/q^0
• B. E = F/q
• C. E = qF
• D. E = ∇F

Answer: (B)

Electric field describes the force that a charge would experience per unit charge placed in the field. If a test charge q experiences a force F, the field is defined by the relation F = qE, so rearranging gives E = F/q. This means the field is a property of space that tells you how much force a unit positive charge would feel at a point, independent of the test charge’s size (as long as you’re using a test charge). Why the other forms don’t fit: E = F/q^0 would equal F, which wrongly makes the field equal to the force regardless of the test charge. E = qF would imply the field scales with the charge itself, which is not how fields are defined. E = ∇F would be the gradient of some scalar function, not the standard relation between force and field; the electric field is related to the negative gradient of the electric potential, not the gradient of force.

Electric field describes the force that a charge would experience per unit charge placed in the field. If a test charge q experiences a force F, the field is defined by the relation F = qE, so rearranging gives E = F/q. This means the field is a property of space that tells you how much force a unit positive charge would feel at a point, independent of the test charge’s size (as long as you’re using a test charge).

Why the other forms don’t fit: E = F/q^0 would equal F, which wrongly makes the field equal to the force regardless of the test charge. E = qF would imply the field scales with the charge itself, which is not how fields are defined. E = ∇F would be the gradient of some scalar function, not the standard relation between force and field; the electric field is related to the negative gradient of the electric potential, not the gradient of force.