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TOPIC 2 Electric Fields www.cbooth.staff.shef.ac.uk/phy101E&M/. Fields & Forces. Coulomb’s law Q r q How does q “feel” effect of Q ? Q modifies the surrounding space. Sets up electrostatic field E Force on charge q is F = q E E due to point charge Q is.

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TOPIC 2 Electric Fields cbooth.staff.shef.ac.uk/phy101E&M/

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Topic 2 electric fields cbooth staff shef ac uk phy101e m

TOPIC 2Electric Fieldswww.cbooth.staff.shef.ac.uk/phy101E&M/


Fields forces

Fields & Forces

  • Coulomb’s law

  • Qrq

  • How does q “feel” effect of Q?

    • Q modifies the surrounding space.

    • Sets up electrostatic field E

    • Force on charge q is F = qE

    • E due to point charge Q is


Electrostatic field lines

Electrostatic Field Lines

  • Like chargesUnlike charges

  • Field lines:

  • Start on positive charge, end on negative

  • Number proportional to charge

  • Strength of field = density of field lines

  • Direction of force at point = tangent to field line.


Conductors

Conductors

  • Charges flow in response to a field

  • Equilibrium  no net field within a conductor

  • Free charges only exist on surface

  • Consider components of field at surface:

    • Charge flows until E// = 0

    •  ETot is always perpendicular to surface of conductor


Continuous charge distributions

Continuous Charge Distributions

  • Divide into charge elements dq

  • Use superposition

  • In practice, express dq in terms of position r

     Use charge density

    3Ddq =  dVdV = element of volume

    2D surfacedq =  dAdA = element of area

    1D linedq =  dd = element of length


Topic 2 electric fields cbooth staff shef ac uk phy101e m

Example 1

A rod of length L carries a charge Q distributed uniformly along its length. If it is centred on the origin and oriented along the y-axis, what is the resulting electric field at points on the x-axis?

Solution available on web page

Example 2

A charge Q is uniformly distributed along the circumference of a thin ring of radius R. What is the electric field at points along the axis of the ring?

For next lecture: revise binomial theorem.


Electric dipoles

Electric Dipoles

Pair of equal & opposite charges, Q & –Q, separated by distance d

Dipole moment (vector)p = Qd(direction is from negative to positive charge)

Total charge is zero, but still produces and experiences electric fields

In uniform electric field, dipole experiences a torque (though no net force)


Topic 2 electric fields cbooth staff shef ac uk phy101e m

Pair of equal & opposite forces F = QE

Perpendicular separation between lines of forces = d sin 

Torque  = F d sin  = Q E d sin  = p E sin 

As vector,  = p  E

i.e. torque acting about centre of dipole, tending to rotate it to align with electric field


Topic 2 electric fields cbooth staff shef ac uk phy101e m

Would have to do work to rotate dipole away from aligned position – stored as potential energy.

Dipole does work (loses energy) rotating towards aligned position.

Define zero of potential energy when dipole is perpendicular to field –  = 90°.

Rotating to position shown, each charge does work: work =forcedistance = Fd/2 cos

Energy of dipole U = – pE cos  = – p.E


Topic 2 electric fields cbooth staff shef ac uk phy101e m

Example 1

What is the electric field at points on the x-axis due to a dipole formed by a charge Q at x = a/2 and a charge –Q at x = –a/2 , for values of x >> a?

Example 2

Two dipoles, with the same charge and separation as above, are placed parallel and a distance  apart:(a) parallel to the line of the dipoles (b) perpendicular to the line of the dipoles.In which case is the force between the dipoles greatest?Part (b) is HARD!!


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