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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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Use charge density
3D dq = dV dV = element of volume
2D surface dq = dA dA = element of area
1D line dq = d d = element of length
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
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.
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)
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
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 =forcedistance = Fd/2 cos
Energy of dipole U = – pE cos = – p.E
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?
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!!