1/11/12. A Scalar Field. The Electric Field + + A Vector Field

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1 The lectric ield q Coulomb s Law of lectro-static orce: qq k r How does q know of the presence of q? q rˆ A Scalar ield These isolated temperatures sample the scalar field T, but T is defined (and can be measured) everywhere (,y) A Vector ield The lectric 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 q o at point lectric field at point It may be more interesting to know which way the wind is blowing and how fast. Define: SI Unit: N/C Magnitude: Direction: Direction of that acts on a positive test charge

2 lectric ield Observation: The net Coulomb force on a given charge is always proportional to the strength of that charge. q test charge q q q q q q rˆ rˆ 4πε r r Define the electric field, which is independent of the test charge, q, and depends only on position in space: q and q in are the sources of the electric field, q is the test charge lectric ield due to Multiple oint Charges To find the resultant field from n point charge: so the electric field is, by definition, given by q q q q rinciple of Superposition! lectric ield Summary lectric field is generated by any charged object. lectric field is a vector field and obeys the principle of superposition, i.e., the field of a system of charged objects is equal 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. lectric ield Lines A visualization tool to illustrate the geometry of an electric field. lectric 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.

3 lectric field due to a oint Charge represents various positive test charges. The force acting on a test charge, q o is: The electric field at any point a distance r from the charge,q : represents various electric field vectors. Note the change in length of with distance r from the positive charge. qq rˆ 4πε r q rˆ q 4 r πε lectric ield Lines lectric : opposite signs but equal magnitude DMO Two ositive Charges: with equal magnitude lectric ield Lines Opposite Charges: unequal magnitude # lines proportional to the magnitude of charge ar from charges, the field lines are as if they are due to a point charge of qqq lectric ield due to an lectric rom symmetry r - r d q - q - z center must lie on dipole ais Use Bionomial pansion & d << z, the magnitude of the electric field at :

4 lectric ield due to an lectric qd πε o z lectric Moment r - r d q - q - z center The electric dipole moment (C-m): p qd p Direction of p is from - negative to positive Rewrite magnitude of electric field at : moment: p q 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. lectric in a uniform electric field q lectric dipole in a uniform electric field τ p When o or 8 o,. However, 8 o is unstable. DMO Because the field is uniform, the net force is zero. However, there is a net torque. 4

5 A oint Charge in a Uniform ield An particle of charge q injected in a field will eperience a force given by q. The resulting acceleration can be found from Newton's second law. DMO oint Charge in Uniform field m a mq a q m q v In a region of uniform field, the particle will eperience a constant acceleration and the resulting parabolic trajectory. v v y a y t v t oint Charge in Uniform field If N/C v 5 5 m/s.5 m Then t v qt y m y m 5 5 m / s C N / C ( (.67 Kg) m v s 6 s) 5