A parrallel plate capacitor has circular cross-section with a radius R and has a charge that varias Q(t). Take the spacing between the plates to be small so that you can assume the electric field is uniform for r < R and vanishes for r>R. Answer in terms of Q(t) and its derivatives. (a) What is the magnitude of the electric field inside the capacitor as a function of time? (b) Inside the capacitor (for r

(a) An insulating sphere carries a charge that is spread uniformly throughout its volume. A con- ducting sphere of the same size carries the same charge, but it is spread over its surface only with no charge in the interior (as it must for a conductor!) Compare the electric fields outside the insulator to the field outside the conductor. Compare the electric fields inside the insulator to the field inside the conductor. (b) Part (a) is an example of a general rule: A charge distributed through some volume will always produce an electric field whose value is a continuous function of position as we cross out of the charge (as we did going from inside to outside of the uniformly charged insulating sphere.) A charge that is distributed across an area (a thin layer of charge with surface charge density o) will produce a field whose value is a DIScontinuous function of position, and the discontinuity is only in the component that is perpendicular to the area and has a value equal to o/€0.…

a) An insulating sphere carries a charge that is spread uniformly throughout its volume. A con- ducting sphere of the same size carries the same charge, but it is spread over its surface only with no charge in the interior (as it must for a conductor!) Compare the electric fields outside the insulator to the field outside the conductor. Compare the electric fields inside the insulator to the field inside the conductor. (b) Part (a) is an example of a general rule: A charge distributed through some volume will always produce an electric field whose value is a continuous function of position as we cross out of the charge (as we did going from inside to outside of the uniformly charged insulating sphere.) A charge that is distributed across an area (a thin layer of charge with surface charge density o) will produce a field whose value is a DIScontinuous function of position, and the discontinuity is only in the component that is perpendicular to the area and has a value equal to o/eo.…

A charge distribution has the charge density given by p =Q{s(x– x,)- 8(x+ x, } . For this charge distribution the electric field at (2x,,0,0)