12.3.1 Electric Field

An electric field is a region of space where electrical forces are exerted on charges. In other words, if a charge is situated in an electrical field, it is going to experience an electrical force.

The electrical field strength E (at a point in an electrical field) is defined as the electrical force per unit POSITIVE charge[1] (at that point). In theory (and in practice), we can test the strength of the field at a particular position by placing a positive test charge q at that position. If the charge experiences an electrical force Fe, then E can be calculated as

\displaystyle E=\frac{{{{F}_{e}}}}{q}

The direction of E is in the same direction as Fe (since we used a positive test charge)

Conversely, if a charge q is situated at a position where the electrical field strength is E, it will experience an electrical force of magnitude

\displaystyle {{F}_{e}}=qE

If q is a positive charge, it will experience an electrical force in the same direction as E (that’s how the electric field strength is defined!). If q is a negative charge, it will experience an electrical force in the opposite direction of E.

Take for example a uniform electric field of strength \displaystyle E=2.0\text{ N }{{\text{C}}^{{-1}}} and direction rightward. A +3.0 pC charge placed in the field will experience a rightward electric force of \displaystyle \displaystyle {{F}_{e}}=qE=(3.0\times {{10}^{{-12}}})(2.0)=6.0\text{ pN}. A −3.0 pC charge however will experience a leftward 6.0 N electric force.

To include the sign or not?

You should leave out the signs when plugging numbers into \displaystyle {{F}_{e}}=qE. In other words, use the formula to calculate the magnitude only. Use logic to figure out the direction. It is less confusing this way.

Video Explanation

Electric Field

Concept Test

2211

Applet

Charges and Fields (PhET)


[1] Since the direction of electrical force experienced by a positive charge is opposite in direction to that experienced by a negative charge (placed at the same position in the electric field), we have to specify the polarity of the test charge in order to define the direction of the electric field. As usual, the positive charge is chosen over the negative charge.

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