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Electric Field
When a charge is kept in space, it will create two things around it. They are electric field and electric potential.
Due to electric field in space, a charge kept in this space will experience electrostatic force. Due to electric potential, work will be done on any charge during its motion.
Strength of the electric field is called electric field strength. Higher the electric field strength at a point, greater the electrostatic force on a charge kept at that point. In space, different points can have different magnitudes of electric field strengths.
Electric field strength (E) at a point is defined as the electrostatic force per positive coulomb charge. Mathematically, electric field strength is given by:
According to this definition, its unit is NC-
Electric field is a vector quantity. Direction of the electric field at a point is defined as the direction of the electrostatic force acting on a positive test charge kept at that point.
Test charge is a tiny positive charge which does not disturb the existing electric field in that region.
Fig (i) Always the direction of the electric field created by a positive charge will be directed away from the positive charge.
Fig (ii) Always the direction of the electric field created by a negative charge will be directed towards the negative charge.
Coulomb’s law
Coulomb’s law says that the electrostatic force between two point charges is directly proportional to each charge and inversely proportional to square of the distance between them.
According to Newton’s third law, the electrostatic force on Q 1 and Q 2 will have the same magnitude and they will be in opposite direction to each other. Therefore
Where, Ɛo is called permittivity of free-space. Permittivity is the measure of a material's ability to store or permit electric field in it. Different type of material has different permittivity. For free-space, it is 8.85× Fm-^1. ‘F’ indicates Farad and it is the SI unit of capacitance.
Metals have infinite permittivity as they completely negate the electric field inside their bulk. I.e. infinite resistance to setting up of field and hence infinite permittivity.
The charge Q 1 will create electric field around it and when this electric field interacts with the charge Q 2 , then the charge Q 2 will experience electrostatic force. Similarly, the charge Q 2 will create electric field around it, and when this field interacts with Q 1 , then the charge Q 1 will experience electrostatic force.
Note: When you use the above equation, include the sign of the charge also. If the force has negative sign then it’s an attractive force. If the force has positive sign then it’s a repulsive force.
When charge is evenly distributed on the surface of a sphere, then we can assume that, this whole charge is concentrated at the centre of the sphere and we can use the above equation as shown below.
Practice Questions
1. A Hydrogen nucleus is at a distance of 10 cm from a point charge of 20. Charge of a Hydrogen nucleus is and its mass is. (i) Find the initial acceleration of the Hydrogen nucleus (ii) If the Hydrogen nucleus is free to move, the sketch a graph of acceleration against distance of it from its initial position. 2. A neutral Hydrogen atom consists of a proton in its nucleus and an electron in its orbit around the nucleus. Distance of the electron from the nucleus is almost. Mass of an electron is and its charge is (i) Find the centripetal force on the electron and state the origin of this force (ii)Find the speed of the electron (iii) Find the time taken by the electron to complete one orbit around the nucleus 3. PQRS is a square and the length of one side is 5 cm. Two charges of and are kept fixed at P and Q respectively. (i) Find the resultant electric field strength at point S and find its direction with the side SR (ii) A charge of is now placed at the point S. Find the resultant electrostatic force on this charge and state its direction. 4.
Two charges are placed at the points R and S respectively. The point Q is at a distance of 10 cm from both R and S. Both QR and QS makes an angle of 30o^ with the line QP. (i) Deduce the resultant electric field strength at the point P (ii) Find the resultant electric field strength at the point Q and its direction (iii) A charge of is now placed at the point Q. Find the resultant electrostatic force on this charge and its direction.
Electric field lines
Direction of an electric field line at a point indicates the direction of the resultant force acting on a positive test charge kept at that point. Electric field lines have the following properties: An electric field line always start from a positive charge and moves towards a negative charge Electric field lines never cross each other Number of filed lines per unit area in a region indicates the strength of the field in that region. In a stronger field, field lines will be much closer to each other. Positive charge always experiences the electrostatic force along the direction of the field line and a negative charge experiences electrostatic force in opposite to the direction of electric field.
Radial electric field and uniform electric field
In radial electric field, the field strength will be different at different points. That is, at different regions, the number of field lines per unit area will be different. Point charge produces radial field.
In uniform electric field, the field strength will be the same at all points. Therefore, electric field lines will be parallel to each other and equally spaced. In the region between oppositely charged parallel plates, uniform field will be created.
