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Electric Field
Potential Gradient and Electric Field Strength
When a charge Q is kept in space, it will create electric potential around it everywhere. The electric potential created by this charge Q will be different at different distances from it. Similarly, when an object is charged (by rubbing), then it will create electrical potential around it. If we keep two or more charged objects in space, then the electric potential at a point in space will be the resultant potential of the potential created by each charged objects. So, there will be potential difference between two points in space. Mathematically, it can be shown that the rate of change of potential difference ( with respect to distance between two closer points gives the electric field strength in that region.
This is called potential gradient.
This concept is used in uniform electric fields. When two parallel metal plates are connected to a battery, the plate which is connected to positive terminal will become positively charged and the plate which is connected to negative terminal will become negatively charged. In the region between these two parallel plates uniform electric field will be created. That is, the strength of the electric field will be the same at all points in the region between the plates.
In uniform electric field , X and Y are two different points. The distance between these two points is d and the potential difference between them is V. The electric field strength in this uniform field is E. Then,
This equation is used only for uniform electric field. Generally we use this equation to find the electric field strength in the region between the oppositely charged parallel plates. Distance between oppositely charged parallel plates is d and the potential difference between them is V. Distance between X and Y is d 1 and the potential difference between them is V 1. Distance between L and M is d 2 and the potential difference between them is V 2. Since the electric field is uniform,
Work done in Electric Field.
If the potential difference between two points in space is V, then the Work done when a charge Q moves between these two points is given by,
Where, V is the potential difference between the two points.
When a positive charge Q moves along the direction of an electric field, then work will be done on the charge and it will gain kinetic energy. Gain in K.E. = QV When a positive charge moves in opposite direction to electric field, then the charge will lose K.E. Loss in K.E. = QV When a negative charge Q moves in opposite direction to an electric field, then work will be done on the charge and it will gain kinetic energy. Gain in K.E. = QV When a negative charge Q moves along the direction of an electric field, then the charge will lose K.E. Loss in K.E. = QV
Practice Questions 1.
Each sphere has a mass of 20 grams and carries a charge of 50 μC. The angle between the two strings is 14o (i) Draw a free-body force diagram for the sphere on the left (ii) Calculate the electrostatic force of repulsion acting on it. (iii) The centers of the spheres are 20 cm apart. Calculate the value for Coulomb’s constant in air.
2. Two long parallel metal plates are 5 cm apart and the potential difference across them is 1kv. (i) Calculate the electric field strength between the plates (ii) An electron (charge -1.6×10-19^ C), is placed centrally between the two plates. Calculate the electrostatic force acting on the electron
Two oppositely and equally charged parallel plates AB and CD are kept horizontally at a distance of 6cm apart. An electron enters horizontally, along the mid region of the two parallel plates, at a speed of 5×10^4 ms-1^ and then it hits the plate AB at a distance of 8 cm from A. (i) Find the time taken by the electron to reach the plate AB after entering between the plates. (ii) Find the electrostatic force experienced by the electron towards the plate AB (iii) Find the potential difference between the two plates.
Useful Videos related to Experiments.
You can watch the following videos related to lab experiments in YouTube.
1. Online Experiment to verify the principle of conservation of momentum: https://youtu.be/hYiWuGiBZjs 2. Online Experiment to verify elastic collisions: https://youtu.be/uW0nPporLA 3. Online Experiment in circular motion: https://youtu.be/EB4poDIsY 4. Online experiment in Coulomb’s law: https://youtu.be/B5LVoU_a08c 5. Online Experiment in Force on electron due to electric field: https://youtu.be/PpOAlj7sOEc
A B
C D
