* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Quantum ElectroDynamics
Survey
Document related concepts
History of quantum field theory wikipedia , lookup
Circular dichroism wikipedia , lookup
Fundamental interaction wikipedia , lookup
Casimir effect wikipedia , lookup
Work (physics) wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Anti-gravity wikipedia , lookup
Magnetic monopole wikipedia , lookup
Electromagnetism wikipedia , lookup
Speed of gravity wikipedia , lookup
Mathematical formulation of the Standard Model wikipedia , lookup
Maxwell's equations wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Lorentz force wikipedia , lookup
Field (physics) wikipedia , lookup
Transcript
TOPIC 2 Electric Fields www.cbooth.staff.shef.ac.uk/phy101E&M/ 1 Fields & Forces Coulomb’s law Q r q F qQ 40r ˆ r 2 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 E Q 40r ˆ r 2 2 Electrostatic Field Lines Like charges Unlike 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. 3 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: Eext E E// + + + + + Charge flows until E// = 0 ETot is always perpendicular to surface of conductor 4 Continuous Charge Distributions Divide into charge elements dq dE Use superposition E dq 40r ˆ r 2 4 r dq ˆ r 2 0 In practice, express dq in terms of position r Use charge density 3D 2D surface 1D line dq = dV dV = element of volume dq = dA dA = element of area dq = d d = element of length 5 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. 6 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) 7 Eext + d F F θ – 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 8 Eext + d F F θ – 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 = F d/2 cos 9 Energy of dipole U = – p E cos = – p.E 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!! 10