Electric displacement vector

Electric displacement vector. See attached file for full problem description.

Charge equation

Please explain in full and do not skip steps thanks

Resitance and Reistivity: Truncated conical cylinder

see attached

Conductivity of Earth: Two hemispherical electrodes in earth.

Please see the attached file.

equations of motion

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Magnetic field

1. A long cylindrical beam (with circular cross section) of charged particles has velocity v in the axial direction. The beam has a uniform charge density f (assume fixed). Find B inside and outside the beam as a function of distance from the axis, in terms of given quantities.

please see attachment below

Answer only question number (3). Please give detailed solution

Charge problem

(See attached file for full problem description)

Cap charges

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Coulomb's Law

Three identical charges +q and a fourth charge -q form a square of side a. a) Find the magnitude of the electric force on a charge Q placed at the center of the square. b) Describe the direction of this force.