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Lesson 4, Topic 4
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# Potential Difference

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When two points A and B are connected in an electric field, more work is done in bringing a unit positive charge from infinity to A than to B, there is potential difference (p.d) between A and B and this difference is equal to the work done in moving the positive charge from B to A against electric field.

Therefore, potential difference between two points is the work done in taking a unit positive charge from one point to the other in the electric field.

The unit of potential difference is volt.

W = qV

V = $$\frac{W}{q}$$Â

Electric field intensity (E) can also be defined as

E =Â  $$\frac{V}{d}$$

d = distance between two points in an electric fieldÂ

Â Therefore, V = Ed _______________ (1)

E = $$\frac{Q}{4 \pi \varepsilon_0 r^2}$$

or

V =Â $$\frac{Q}{4 \pi \varepsilon_0 d^2} \scriptsize \; \times \; d$$

Substituting this in equation 1

Or V =Â  $$\frac{Q}{4 \pi \varepsilon_0 d}$$

V is the potential due to a charge q at a distance d from the charge.

Examples

1. A point charge of magnitude 2 x 10-6C is moved through a distance of 0.50m against a uniform electric field intensity 50vm-1. What is the workdone on the charge?

Solution

E =$$\frac{F}{q}$$Â  Â  Â  Â  Â  , F=QE

Work done = FÂ x d

Â Â  Â  Â  Â  Â  Â  Â  Â  = EqÂ x d

Â  Â  Â  Â  Â  Â  Â  Â  = 30 xÂ 2 x 10-6 0.50

Â Â  Â  Â  Â  Â  Â  Â  Â  = 3.0Â x 10-5 J

2. Two parallel plates are charged to a voltage of 50v. If they are separated by a difference of 10.0cm, calculate electric intensity between them.

Solution

E =Â $$\frac{v}{d} = \frac{50}{0.1}$$Â

=500vm-1

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