6-The electric potential

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29 Terms

1

What is the expression for work done by an external force to move a charge q in an electric field E?

ds= the displacement element along the path.

<p>ds= the displacement element along the path.</p>
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2

What is the significance of the dot product E⋅ds in the work done equation?

It ensures that only the component of the electric field along the displacement contributes to the work done.

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3

Why is the work done independent of the path taken?

  • The work is the same for any path because the electric field is conservative.

  • This means the work depends only on the initial and final positions, not on the path taken.

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4

How can you visualise path independence in an electric field?

Any path can be decomposed into:

  1. Circular arcs perpendicular to E → No work done.

  2. Radial sections parallel to E → Same work as the straight-line path.

    Thus, work is independent of the path.

<p>Any path can be decomposed into:</p><ol><li><p><strong>Circular arcs</strong> perpendicular to <strong>E</strong> → No work done.</p></li><li><p><strong>Radial sections</strong> parallel to <strong>E</strong> → Same work as the straight-line path.<br></p><p>Thus, work is independent of the path.</p></li></ol><p></p>
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5

What does it mean for the electric force to be conservative?

  • It means that the work done in moving a charge between two points is independent of the path taken

  • The total work done in a closed loop is zero.

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6

What does path independence imply in the context of electric fields?

Path independence means that the work done in moving a charge qqq between two points is the same, regardless of the path taken, as the electric field is conservative.

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7
<p>What is the result when the work done along two different paths Γ<sub>1​</sub> and Γ<sub>2</sub>​ is considered?</p>

What is the result when the work done along two different paths Γ1​ and Γ2​ is considered?

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8

What is the Circuital Law?

  • The Circuital Law states that the line integral of the electric field along any closed path is zero

  • This applies to static electric fields.

<ul><li><p>The Circuital Law states that the line integral of the electric field along any closed path is zero</p></li></ul><p></p><ul><li><p>This applies to static electric fields.</p></li></ul><p></p>
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9

What does the circle in the notation ∮E⋅ds represent?

It indicates that the integral is taken along a closed path

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10

What is the difference between the circuital law and Gauss’s law?

  • The circuital law is a line integral around a closed path for a static electric field.

  • Gauss’s law involves a surface integral over a closed surface related to the electric flux.

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11

What are Gauss’s Law and the Circulation Law equivalent to?

Gauss’s Law and the Circulation Law together are equivalent to Coulomb’s Law in electrostatics.

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12

What is the electric field inside a hollow conductor?

The electric field inside a hollow conductor is zero, regardless of the conductor's shape.

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13

Why is the electric field inside a hollow conductor zero?

Because all excess charge resides on the outer surface, and there is no charge on the inner surface.

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14

What happens if there were both positive and negative charges on the inner surface of the hollow conductor?

  • It would lead to a non-zero circulation of the electric field

  • This would violate the Circulation LawE⋅ds=0

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15

What does the electric potential represent?

The electric potential at a point is the potential energy per unit charge at that point in an electric field.

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16

How is the work done in moving a charge related to the potential energy?

  • The work done in moving a charge q from point A to point B is equal to the change in potential energy of the charge.

  • This is path-independent.

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17
<p>What is the expression for potential energy at point B?</p>

What is the expression for potential energy at point B?

  • Γ is any path from A to B.

<ul><li><p> Γ is any path from A to B.</p></li></ul><p></p>
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18
<p>What is the definition of electric potential V<sub>B</sub> at point B?</p>

What is the definition of electric potential VB at point B?

This is valid for any path between A and B.

<p>This is valid for any path between A and B.</p>
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19

What are the units of electric potential V?

Volts

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20

How does the superposition principle apply to electric potential?

It states that the electric potential at a point due to multiple charges is the algebraic sum of the potentials due to each individual charge.

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21

What is the formula for potential difference (p.d.) between two points B and C?

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22

What is the significance of the potential difference between two points?

It represents the work needed to move a unit charge from one point to another

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23

What is the reference point for electric potential around a point charge?

It is conventionally taken to be at infinity, where the potential is defined as zero.

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24

What is the formula for the electric potential at a distance R from a point charge Q?

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25

What is an equipotential surface?

  • Its a surface where all points have the same electric potential.

  • No work is required to move a charge along this surface.

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26

What is the relationship between the electric field and equipotential surfaces?

  • The electric field is always perpendicular to an equipotential surface at every point.

  • No work is done when a charge moves along an equipotential because the electric field does no work in that direction.

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27

What happens to the potential when the electric field is zero?

  • When the electric field is zero, the potential must be constant.

  • This is true for any region with no electric field, such as inside a conductor.

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28

Why are conducting surfaces equipotential surfaces?

Because the electric field inside a conductor is zero in electrostatic equilibrium, meaning the potential must be constant throughout the conductor.

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29

What can we deduce about the electric field just outside a conductor?

  • The electric field just outside a conductor must be perpendicular to the surface because the conductor is an equipotential surface

  • The electric field must be normal to equipotential surfaces.

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