Electric field lines never form closed loops as they are conservative in nature. Explain how? What is the link between being conservative and not forming closed loops?
Electric field lines never form closed loops as they are conservative in nature. Explain how? What is the link between being conservative and not forming closed loops?
A force is said to be conservative if its work along a trajectory to go from a point A to a point B is equal to the difference U(A) − U(B) where U is a function called potential energy. This implies that if A = B then there is no change in potential energy. This fact is independent of the increase or not of the kinetic energy. If a conservative force were to form loops, it could provide a non-zero network (because the direction of the force could always be the same as that of the looping trajectory) to go from A and then back to A, while at the same time its conservative character would ensure that this work should be zero; which is a contradiction. 'Hence, "conservative force" and "forming loops" are two incompatible properties that cannot be satisfied at the same time. And electrostatic fields are conservative in nature and hence do not form closed loops.
Electric field lines are the path traced by a unit positive charge when left free in an electric field" and tangent to field lines gives the direction of electric field. So if they will form close loops then the tangent at any point will direct in different directions which is not possible. Also, the unit positive charge moves only due to the force of repulsion and attraction and as a result traces only definite path, not the circular path.
A force is said to be conservative if its work along a trajectory to go from a point A to a point B is equal to the difference U(A) − U(B) where U is a function called potential energy. This implies that if A = B then there is no change in potential energy. This fact is independent of the increase or not of the kinetic energy. If a conservative force were to form loops, it could provide a non-zero network (because the direction of the force could always be the same as that of the looping trajectory) to go from A and then back to A, while at the same time its conservative character would ensure that this work should be zero; which is a contradiction. 'Hence, "conservative force" and "forming loops" are two incompatible properties that cannot be satisfied at the same time. And electrostatic fields are conservative in nature and hence do not form closed loops.
Electric field lines are the path traced by a unit positive charge when left free in an electric field" and tangent to field lines gives the direction of electric field. So if they will form close loops then the tangent at any point will direct in different directions which is not possible. Also, the unit positive charge moves only due to the force of repulsion and attraction and as a result traces only definite path, not the circular path.
