☰ Contents · Physics

Field of a charged sphere and potential

Lessons 31–32 · 2 lessons · N. Sh. Turdiyev, K. A. Tursunmetov, A. G. Ganiyev, K. T. Suyarov, J. E. Usarov, A. K. Avliyoqulov. Physics Grade 10, 1st edition. Niso Poligraf Publishing House, Tashkent, 2017
32

Potential of a point charge’s field. Potential difference

Textbook: pp. 120–122
GoalUse the potential of a point charge’s field, potential difference (voltage), the relation E = U/d and equipotential surfaces in problems.
New words
potential · potensialpotential difference (voltage) · potensiallar farqi (kuchlanish)volt · voltequipotential surface · ekvipotensial sirt
Explanation

If the field strength is the force characteristic of the field, the potential is its energy characteristic: φ = W/q₀, where W is the potential energy of a test charge q₀ in the field. At distance r from a point charge q in vacuum φ = kq/r (φ = 0 at infinity); potential is a scalar, with the same sign as q, and the potentials of several charges add algebraically. Its unit is 1 V = 1 J/C. When a charge moves from point 1 to point 2 the field does work A = q(φ₁ – φ₂) = qU, where U = φ₁ – φ₂ is the potential difference (voltage). In a uniform field E = U/d (unit 1 V/m = 1 N/C). A surface of equal potential is an equipotential surface; for a point charge these are spheres around it. Field lines are always perpendicular to equipotential surfaces and point toward decreasing potential; moving a charge along an equipotential surface requires zero work.

Worked examples
At r = 0.3 m from q = 6 nC, φ = kq/r = 9·10⁹·6·10⁻⁹/0.3 = 54/0.3 = 180 V. If φ = 60 V at a second point, U = 180 – 60 = 120 V.
A 4 nC charge moves between two points with a potential difference of 150 V: A = qU = 4·10⁻⁹·150 = 6·10⁻⁷ J = 600 nJ. If the plates are 3 cm apart, E = U/d = 150/0.03 = 5000 V/m.
Class activity

Only in class: on A4 paper mark a positive charge and draw around it its equipotential lines (concentric circles) and field lines (radial). No electrical equipment is used.

Practice
1
State the definition and unit of potential.
2
What is the potential at r = 0.6 m from q = 4 nC (V)? (k = 9·10⁹)
3
A charge of 2 nC moves through a potential difference U = 50 V. What is the work of the field (nJ)?
4
The plates are 5 cm apart with a voltage of 200 V. What is E (V/m)?