Electric field

Al electric field is a region around an electric charge where an electric force is experienced. This can be mapped out by electrostatic lines of force.

A line of force is a line such that the tangent to it at any point is in the direction of the force on a small positive charge at that point. Arrows are drawn the direction and these point from positive towards or inwards to the negative charge. A collection of lines of force is called an electric flux.

 Electric field pattern

6. Two equal oppositely charged parallel plates

 

Definition

1. A neutral point in an electric field is a point where the resultant electric field field intensity is zero.

The force exerted on the charged body in an electric field depends on the charge on the body and the intensity or strength of the field.

2. Electric field intensity or strength is defined as the force exerted on a positive charge of 1 coulomb placed at a point in electric field

Therefore, electric field intensity, E is a vector quantity

The S.I. unit of E is NC^-1

Consider the diagram below

Placing a small charge Q₀ at point P, in an electric field, the force at P due to Q is given by

 

Note E is directed away from a positive charge and directed towards the negative charge.

Example 1

Find the electric field intensity at P

Solution

Solution

Example 2

Three point charges of +6.4μC, -6.4μC and +3.2μC are arranged in line at points  A, B, and  C respectively as shown in diagram above. Find the electric field intensity at P.

Solution

Hence the electric field at P is 1.472 x 10⁵ NC^-1 to the right

Example 3

Two point Charges P and S of -17.6μC and -9.0μC respectively are placed in a vacuum at a distance of 21cm apart. When a 3^rd charge R is placed midway between P and S as shown in figure above, then, the net force at S is zero

(i) Determine the charge on R

(ii) Calculate the electric potential at position R.

(iii) Sketch the electric field lines corresponding to charge distribution

Solution

(ii) Electric field potential, at a distance r fro charge D is given by

Example 4

Calculate the electric field intensity midway between Q1 and Q2

Solution

Example 5

Charges Q₁ and Q₂ of -5μC and +2.0μC respectively are placed at two opposite corners of a rectangle of sides 5.0cm and 10.0cm as shown below

Calculate the electric field at A

Solution

Hence the electric filed intensity at A is 8.49 x 10⁶ NC^-1 at 58⁰ to the horizontal

Example 6

Two point charges A and B of +10μC and +0.05μC are separated by a distance of 8cm along the horizontal as shown above. Find the electric field intensity at P.

Hence the electric field intensity at A is 3.55 x 10⁵NC^-1 at 66⁰ to the horizontal

Example 7

Find the electric field intensity at P.

Solution

Hence the electric field intensity at P is 1.98 x 10² NC^-1 at 450 to horizontal

Example 8

Two point charges are separated by 10cm in air as shown

Solution

Hence the electric field intensity at P is 4.5 x 10⁵ NC^-1 at 0⁰ to the horizontal

Example 9

Two points +3.8μC and -5.2μC are place in air at points A and B as shown. Determine the electric field intensity at C

Solution

Hence the electric field intensity at C is 1.89 x 10⁷NC^-1 acting at 29.7⁰ to horizontal.

Example 10

Three charges of -3 x 10^-9C, +4 x 10^-9C and +3 x 10^-9C are placed at vertices A, B, C respectively of a rectangle ABCD of side 3cm x 4cm as shown. Calculate the resultant electric field intensity at D

Solution

Hence electric field intensity at D = 3.09 x 10⁵NC^-1 at 89⁰ to horizontal

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Compiled by Dr. Bbosa Science