Magnitude of the electric field; distribution of the charge

Please show all work and show all equations used and diagrams.

1) Positive charge Q is distriibuted uniformally throughout an insulating sphere of radius R, centered at the origin. A particle with a positive charge Q is placed at x = 2R on the x axis. The magnitude of the electric field at x =R/2 on the x axis is:

2) Charge is distributed uniformally along a straight wire. the electric field 2 cm from the wire is 20N/C. The electric field 4cm from the wire is:

3) Positve charge Q is placed on a conducting sphereical shell with inner radius R1 and outer radius R2. A particle with charge q is placed at the center of the cavity. The magnitude of the electric field at a point in the cavity, a distance r from the center, is:

Solution Preview

1) Positive charge Q is distriibuted uniformally throughout an insulating sphere of radius R, centered at the origin. A particle with a positive charge Q is placed at x = 2R on the x axis. The magnitude of the electric field at x =R/2 on the x axis is:

Fields are additive The field inside the charged sphere is given by : 1/(4pi Eo) Qr/R^3 where r is the distance out to the surface of the sphere. This follows from Gausses law. Then at x= R/2 this becomes:
1/(4pi Eo) Q/2R^2

The magnitude ...

Solution Summary

The solutions are shown with full calculations and narrative sufficient to understand the problems and solutions.

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