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Understanding the Relationship Between Electric Potential & Electric Field

Explore the correlation between conservative forces, potential energy, electric force, and potential energy in electric fields. Learn how to calculate electric field strength and potential for various setups, including charged spheres and point charges.

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Understanding the Relationship Between Electric Potential & Electric Field

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  1. Relation BetweenElectric Potential V & Electric Field E

  2. The General Relationship between a Conservative • Force & its Potential Energy has the form: • For the Electric Force: • F = qE & U = qV • So, the relationship is:

  3. The simplest case is a Uniform E Field

  4. Example • E field obtained from voltage • Two parallel plates are charged to • produce a potential difference of • 50 V. The plate separation is • d = 0.050 m. • Calculate the magnitude of the electric • field E in the space between the plates.

  5. Example • E field obtained from voltage • Two parallel plates are charged to • produce a potential difference of • 50 V. The plate separation is • d = 0.050 m. • Calculate the magnitude of the electric • field E in the space between the plates. • E = (Vba)/d = (50)/(0.05) • E = 1,000 V/m

  6. Example Charged Conducting Sphere A conducting sphere is uniformly charged with total charge Q. Calculate the potential at a distance r from the sphere’s center for (a) r > r0, (b) r = r0, (c) r < r0 V is plotted here, and compared with the electric field E. Use the relation:

  7. Example Charged Conducting Sphere Calculate the potential at a distance r from the sphere’s center for (a) r > r0, (b) r = r0, (c) r < r0 Use the relation: Vba = - [Q/(4πε0)] ∫[dr/(r2)] Limits ra = to rb

  8. Setting the potential V to zero at r = ∞ gives the General Form of the Potential Due to a Point Charge:

  9. Example: Work required to bring two positive charges close together: • Calculate the minimum work that must be done • by an external force to bring a charge q = 3 μC • from a great distance away (take r = ∞) to a • point 0.500 m from a charge Q = 20 µC.

  10. Example: Work required to bring two positive charges close together: • Calculate the minimum work that must be done • by an external force to bring a charge q = 3 μC • from a great distance away (take r = ∞) to a • point 0.500 m from a charge Q = 20 µC. • W = qV = q(Vb –Va) • = qke[(Q/rb) – keQ(Q/ra)] • 1.08 J

  11. Example: Potential above two charges (a) Calculate the electric potential at point A in the figure due to the two charges shown. (b) Repeat the calculation for point B. (Solution on white board).

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