Question

L. Please give COMPLETE aswers or this probleml! Plesse swer IN THE SPACES PROVIDED. Additional sheets will not be necessary (a) Afler solving a number of simple electrostatic problems beginning with the differential form of Coulomb's Law, we found that the same problems could be solved much more easily by using Gauss' Law for Electric Fields. Similarly, after solving a number of simple magnetostatic problems beginning with the differential form of the Biot-Savart Law, we found that the same problems could be solved much more easily by using Ampere's Circuital Law. What condition must exist such that the simpler form in each case may be used? How does this condition simplify the problem analysis for each case? (Sspmina G) b) What quet in Questions mentioned bi When using Gauss'Law for Electric Fiekds to determine the electric field due to a given charge distribution, it is essential that a correct geometric shape be chosen for the successful application of the law. A similar situation is true to successfully determine the magnetic field due to a given current distribution using Ampere's Circuital Law. Name the general geometric shape required corresponding to each law, and specify the criterion which needs to be satisfied by the geometric shapes for these two laws to be applied most efficiently. (S points) pproaches mentioned in Questions (a) and (b) may be used efficiently? (5 points) O What questions must be answered in order that the simplera

Answer 1

a. Gauss law of electric fields can be used when the gaussian surface chosen is a closed one including the charges within it. However, the gaussian surface must be symmetrical and not an irregular shape.

Similarly, In order to have a simpler situation using Ampere Circuital law, the magnetic field along the amperian loop, being taken into account should have a constant magnetic field. Only, then the simpler formula can be used for determination of the required term, else the complicated integral of the Magnetic field has to be done in order to achieve the same.

b. The geometrical shape required by the Gauss law of electric field should by synmetrical and should enclose the electric charge required to be taken into consideration. It is generally spherical in shape for point charges.

For the Ampere's circuital law, the closed loop required should symmetrically encircle the current carrying conductor ans should in the region of constant magnetic field.

c. The questions asked in case of Ampere's circuital law:

If the current in the conductor is constant?

Is the amperian loop symmetrical and lies within constant magnetic field?

In case of Gauss law of electric field:

Is the gaussian surface chosen symmetrical and encloses the charges?

Are all the charges to be considered taken in the gaussian surface?