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Electric Fields and Electric Potential

Electromagnetism

A charge does not need to touch another charge to push or pull it. It creates an electric field in the space around it, and electric potential describes how much energy a charge would have at each point in that field.

What an electric field is

An electric field is a region where a charge experiences an electric force, and its strength at a point is the force per unit charge placed there. The field is a vector: it points away from a positive charge and toward a negative charge. Field lines give a picture of the field, with closer lines meaning a stronger field and arrows showing the direction a positive test charge would move. Near a single point charge the field falls off as 1/r^2, just like the force in Coulomb's law. Between two parallel charged plates the field is nearly uniform, which is useful in capacitors and in old cathode-ray tubes. A test charge must be small so that it does not disturb the field it is measuring.

Electric potential and voltage

Electric potential is the electric potential energy per unit charge at a point, measured in volts, where one volt equals one joule per coulomb. Voltage is the difference in potential between two points, and it tells you how much energy each coulomb of charge gains or loses moving between them. A positive charge moves naturally from high potential to low potential, losing potential energy as it goes, while a negative charge moves the opposite way. Potential is a scalar, so it has no direction, which makes it easier to add up from several charges than field vectors. The potential around a point charge falls as 1/r, more slowly than the field, which falls as 1/r^2.

Where you see it

Every battery, power supply and wall socket is described by its voltage, and every circuit works because charges move through potential differences. In a television or oscilloscope tube, electrons were accelerated by a large voltage and then steered by electric fields to draw a picture. Van de Graaff generators build up very high potentials that make hair stand on end and produce visible sparks. Lightning rods work by keeping a building near ground potential so that a strike has a safe path to earth. Even the nerve signals in your body involve tiny voltage changes across cell membranes.

Common mistakes

• Treating field as a scalar: field is a vector with direction, while potential is a scalar with only a value.
• Mixing up E and V: E falls as 1/r^2 from a point charge, but V falls as 1/r.
• Thinking voltage is an absolute value: only potential differences matter physically; the zero of potential is a choice, often taken at infinity or at earth.

Practice questions

1. A test charge of 2.0 x 10^-6 C feels a force of 0.040 N. What is the field strength?
   Show answer

   E = F/q = 0.040 / (2.0 x 10^-6) = 2.0 x 10^4 N/C.

2. What is the potential 0.50 m from a +6.0 microC charge?
   Show answer

   V = (8.99 x 10^9)(6.0 x 10^-6)/0.50 = 5.39 x 10^4 / 0.50 = 1.08 x 10^5 V.

3. How much work is done moving 0.50 C through a potential difference of 12 V?
   Show answer

   W = qV = 0.50 x 12 = 6.0 J.

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