Electric Field Due To A Group of Charges

Consider a system of charges q1, q2, ..., qn with position vectors r1,r2, ..., rn relative to some origin O. Like the electric field at a point in space due to a single charge, electric field at a point in space due to the system of charges is defined to be the force experienced by a unit test charge placed at that point, without disturbing the original positions of charges q1, q2, ..., qn.

We can use Coulomb’s law and the superposition principle to determine this field at a point P denoted by position vector r.

Electric field E1 at r due to q1 at r1 is given by

where 1P ˆr is a unit vector in the direction from q1 to P, and r1P is the distance between q1 and P. In the same manner, electric field E2 atr due to q2 at r2 is

 where  ˆr is a unit vector in the direction from q2 to P and r2P is the distance between q2 and P. Similar

expressions hold good for fields E3, E4, ..., En due to charges q3, q4, ..., qn.By the superposition principle, the electric field E at r due to the system of charges is (as shown in Fig)

  

E is a vector quantity that varies from one point to another point in space and is determined from the positions of the source charges.

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Some of these questions which may be asked in your Board Examination 2012-2013

Q1: What is a charge?

Q2: What is the SI unit of Charge?

Q3: What is charge on a neutron?

Q4: what is the change on an electron?

Q5: Explain what is an fundamental electronic charge?

Q6: what is main cause of charging?

Q7: Electrostatic forces are much stronger than gravitational forces. Give one example.

Q8: What is the value of charge on an electron? is a charge less than this value possible?

Q9: What is charge on a photon?

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