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Relation Between Electric Potential V & Electric Field E

Relation Between Electric Potential V & Electric Field E. 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:. The simplest case is a Uniform E Field. Example

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Relation Between Electric Potential V & Electric Field E

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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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