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Electric Charges and Fields

Electric Field

Electric Field: What do you think happens when you feel a shock when you touch an iron handle of a door or maybe another person? Obviously, due to an electric charge. These are charges that are accumulated on the surface after being rubbed against an insulator. That collected charge is able to find a conductor in touch to relieve itself hence causing an electric flow.

But there is also a finding by early scientists that even kept at a distance, two items are always exerting a certain amount of force on each other. Even if one of the charges has its position vacated and then return back to the position, the effect still remains in the area around the two. That charged area has been termed as Electric Field about which we will be exploring in depth.

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Electric Field

Electric Field

Assume there are point charges (sizes <<< r) P and Q placed r distance apart in a vacuum. Both charges create an electric field around them which ultimately is responsible for the force applied by the two on each other. The Electric Field around Q at position r is:

E = kQ / r2

Where r is a unit vector of the distance r with respect to the origin. This value E(r) [SI unit N/C] amounts to an electric field of each charge based on its position vector r. When another charge q is brought at a certain distance r to the charge Q, a force is exerted by Q equal to:

FQ  = kQq/ r2

Now, there is an equal and opposite force exerted on Q by q which is equal to:

Fq  = kqQ/ r2

Hence, if q is a unit charge, the force applied is equal to field value.

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electric charges cheat sheet

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Electric Field due to a System of Charges

If there is a system of charges q1, q2, … qn in space with position vectors r1, r2,rn and the net effect of the Electric Charges are required to be calculated on a unit test charge q with position vector r placed inside the system, then it is attributed to a superimposition of Electric field values for all charges by Coulomb’s Law:

E = E1 + E2 + … + En

= kq1/r12 + kq2/r22 + … + kqn/rn2

where En(rn) is the Electric Field value of charge n in the system with respect to position vector rn. Here, E is a vector quantity and its value are attributed to change in the position of source charges.

Solved Examples for You

Question: Since the actual measurable quantity inside a system is an Electric Force, why has the intermediate notion of Electric Field been introduced at all? Explain its significance.

Solution: The study of electrostatics involves the use of the term electric field which may be convenient to explain the concepts but it is not really necessary. To explain the phenomenon of an electrical environment consisting of a system of charges, we use the term Electric Field.

It is very useful in determining the amount of electric force applied to a unit test charge inside the system. But it also ensures that no change in the characteristics of charges happens due to the test charge. The term field is a strong interpretation of a value or quantity in space wrt the change in position at every point.

Hence, the field is a vector entity. And force is a vector value corresponding to it. There is another important scenario where electric field terminology plays an important role; that is, time-phenomena. Here, if a charge in motion applies force on another charge causing it too to be in motion, then the small time-delay in between can be attributed only to the notion of electric field. The natural notion is very useful in such a scenario in physics.

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