The Electric ield 1 Coulomb s Law of Electro-static orce: k How does 1 know of the presence of? 1 r rˆ sets up an electric field in the space surrounding it. At any point the field has both a magnitude and direction.
A Scalar ield 77 73 7 75 8 71 84 77 80 68 64 83 8 88 55 73 66 75 80 88 88 83 90 9 91 These isolated temperatures sample the scalar field T, but T is defined (and can be measured) everywhere (x,y)
A Vector ield 77 73 8 84 83 88 7 71 80 57 9 75 77 68 64 56 55 73 66 75 80 88 83 90 91 It may be more interesting to know which way the wind is blowing and how fast.
The Electric ield The electric field is a vector field: consists of a distribution of vectors, one for each point in the region around a charged object. Test charge o at point P E Electric field at point P Define: SI Unit: N/C E 0 Magnitude: Direction: E 0 Direction of that acts on a positive test charge
Electric ield Observation: The net Coulomb force on a given charge is always proportional to the strength of that charge. 1 0 test charge 1 1 0 1 rˆ 1 rˆ 40 r1 r Define the electric field, which is independent of the test charge, 0, and depends only on position in space: E 0 1 and in are the sources of the electric field, 0 is the test charge
Electric ield due to Multiple Point Charges To find the resultant field from n point charge: 3 1 so the electric field is, by definition, given by 3 1 0 3 0 0 1 0 E E E E Principle of Superposition!
Electric ield Summary Electric field is generated by any charged object. Electric field is a vector field and obeys the principle of superposition, i.e., the field of a system of charged objects is eual to the (vector) sum of the field of each individual charged object in the system. The electrostatic force between charged objects is mediated by the electric field.
Electric ield Lines A visualization tool to illustrate the geometry of an electric field. Electric field lines originate from positive charges and terminates at negative charges. The direction of the electric field at any location is tangential to the field line there. The magnitude of the electric field at any location is proportional to the density of the lines there.
Electric field due to a Point Charge represents various positive test charges. represents various electric field vectors. The force acting on a test charge, o is: The electric field at any point a distance r from the charge, : Note the change in length of with distance r from the positive charge. 1 4 0 0 r rˆ 1 E 4 r 0 0 rˆ
Electric ield Lines Electric Dipole: opposite signs but eual magnitude Two Positive Charges: with eual magnitude
Electric ield Lines Opposite Charges: uneual magnitude ar from charges, the field lines are as if they are due to a point charge of = # lines proportional to the magnitude of charge
Electric ield rom Two Charges _
Electric ield due to an Electric Dipole rom symmetry E r - r d E - P E - z Dipole center E E 1 4 o E must lie on dipole axis r 1 4 o 4 o (z d ) r 4 o (z d ) Use Binomial Expansion & d << z, the magnitude of the electric field at P: E d o z 3
Electric ield due to an Electric Dipole E P E d E z 3 o r z The electric dipole moment (C-m): r - d - - Dipole center - p p d Direction of p is from negative to positive Rewrite magnitude of electric field at P: E p o z 3
Electric Dipole Moment Dipole moment: p L L is the separation of the two charges The direction of the dipole moment is taken to be from the negative to the positive end of the dipole. p 610-30 C m0.04 e nm
Electric Dipole in a uniform electric field E d sin d sin d sin Ed sin pe sin pe Because the field is uniform, the net force is zero. However, there is a net torue.
Electric dipole in a uniform electric field DEMO 5A-31 pe When = 0 o or 180 o, = 0. pe sin or clockwise rotation However, = 180 o is unstable.
A Point Charge in a Uniform ield An particle of charge injected in a E field will experience a force given by = E. The resulting acceleration can be found from Newton's second law. ma m In a region of uniform E field, the particle will experience a constant acceleration and the resulting parabolic trajectory. a E The control of electrons by so-called deflection plates is the principle behind the operation of the cathode-ray tube used in oscilloscopes and many televisions and computer monitors.
Point Charge in Uniform E field ma E a E m v 0 x - - - - - - - - - - - - - - - - - - E v x v 0 x v 0 t y 1 a y t 1 m E x v o
Point Charge in Uniform E field If E=100N/C v 0 =510 5 m/s x=0.5 m Then P v 0 x - - - - - - - - - - - - - - - - - - E t x v 0 0.5 m 10 510 5 m / s 6 s y Et m 19 1.610 C 10 N / 31 (1.6710 Kg) C (10 6 s) y 4.7910 m
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Potential Energy of an Electric Dipole Potential energy can be associated with the orientation of an electric dipole in an electric field. p E pe sin 0 0 U W d pe sind 90 90 U pe cos U 0 0 Choose 0( 90 ) 0 cos U U pe p E U is least =0 U=-pE U is greatest =180 U=pE U =0 when =90
Electric ield With this concept, we can map the electric field anywhere in space produced by any arbitrary: Bunch of Charges Charge Distribution E 1 4 0 i r i ˆr i E 1 4 0 d i r ˆr - - - - - Net E at origin These charges or this charge distribution source the electric field throughout space
Electric ield due to an Electric Dipole E r P E z p E z 3 o In general: r - d - - Dipole center - p E 1 r 3 *Where r is the distance between the dipole center and the point in uestion. *regardless of wherever the point lies on the dipole axis.