relation between electric field and electric potential
Answers
Explanation:
The relationship between potential and field (E) is a differential: electric field is the gradient of potential (V) in the x direction. This can be represented as: Ex=−dVdx E x = − dV dx . Thus, as the test charge is moved in the x direction, the rate of the its change in potential is the value of the electric field.....
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Answer:
Work done in moving the test charge q0 from a to b is given by-
W(q0a→b)=∫baF⃗ .dl⃗ =q0∫baE⃗ .dl⃗
Where,
F is the force applied
dl is the short element of the path while moving it from a to b.
The force can be written as charge times electric field.
=q0∫baE⃗ .dl⃗
Dividing both sides by test charge q0
wq0=∫baE⃗ .dl⃗
Workdone by the test charge is the potential Va-Vb
∫baE⃗ .dl⃗ =Va−Vb
For equipotential surface, Va=Vb thus,
∫baE⃗ .dl⃗ =0
Hope you understood the relation and conversion between Electric Field and Electric potential.