An electrical field is a non-contact pressure (like gravity or magnetism). TheBritish Physicist Michael Faraday developed the ide by considering apoint fee permeating currently of electrical field in every direction in space. Once another suggest is carried near the (and we usage a very small positive allude charge as a \"test\"charge) the suggest feels a field. This provides an electric field, E, characterized as:


where F is the force exerted top top the charge and q is themagnitude that the charge. Our devices are force per unit charge, or Newtons/Coulomb. Electric field has both magnitude and also direction so that is a vector quantity.

You are watching: E = kq/r^2

We can do some an ext manipulations with this formula. Recall Coulomb\"s legislation (F = kq1q2/r2). If we integrate this and also the meaning of electric field, we get



Note that if Q is positive, that repels the check charge and the ar linesare directed out from the suggest charge. If Q is a an adverse charge, climate the field lines are directed toward the allude charge.

k can also be to express in regards to the permittivity of complimentary space,eo. K = 1/4peo, or


Here is a rapid example:

1. Calculate the magnitude and direction that the electrical field at pointP i beg your pardon is 50 cm to the best of a allude charge Q = - 5.0 x 10-6 C.

Answer: from the picture, we check out our confident test charge on the left andour suggest charge Q top top the right. Because the charge is negative, the field points to carry the dues together. The size of the ar is given by:

E = kQ/r2, or (9 x 10 9 Nm2/C2)(5.0 x 10-6C)/(.50m)2 = 1.8 x 10 5 N/C


If multiple charges or check points room available, the trouble is addressed byfinding the ar at each suggest from an individual charge and also then including the fields using vectors, as shown below:

Q1 and also Q2 both represent negative charges the somemagnitude. E1 and also E2 stand for the individual fields felt by point P native Q1 and also Q2 respectively. The vector at E to represent thetotal electrical field felt at allude P and also is the vector summation of E1 and E2. This is known as the rule of Superposition.

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Field present are provided to indicate the direction of force in all directionsfrom a source. Some an easy rules:


Electric field lines start on hopeful charges and end top top negativecharges. The arrows top top the field lines need to be attracted that way.Lines are attracted so they are perpendicular come the point.Strong fields show much more lines spaced closer together than weakfields.Lines get closer with each other as they obtain closer come thesource.Field lines never ever intersect!

To view some great pictures and read more on the subject,check out few of the following. Over there is a lot of of good stuff here!


The NTNU gives some good applets for Physics. Click right here for an applet that demonstrates charges relocating in electrical Fields.

Also, below is another applet friend can examine out because that ElectricFields: