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The principle of superposition of electric fields
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In accordance with your variant to solve one of the following problems listed below. The number of problem statement and all necessary input data are reduced in the Table 1.1. If there is letter index in the number of the problem statement, then you should only answer the question, which corresponds to this index.
1 The electrostatic field is created with two endless parallel plates, which are charged uniformly with surface densities σ 1 and σ 2. Find force, which acts in this field on the point charge Q 1, if it’s situated:
а) between the planes;
b) outside of planes.
2 The point charge Q 1 is situated in the centre of uniformly charged sphere with a radius R. Find the electrostatic intensity in two points, which lies from the centre at a distance of r 1 and r 2, if:
а) the charge of sphere equals Q 2;
b) surface density of the sphere charge equals σ 2.
3 The long thread, uniformly charged with the linear density τ 1, is situated on an axis of the long cylinder, which has the radius of R. The cylinder is uniformly charged with the linear density of τ 2. Define the electrostatic field intensity in the other points:
1) at a distance of r 1 from the thread;
2) at a distance of l from the surface of cylinder.
4 Two long parallel threads are uniformly charged with the linear densities of τ 1 and τ 2. The distance between the thread is l. Define the electrostatic field intensity at the point, which is situated at a distance of r 1 from the first thread and r 2 from the second thread.
5 The electrostatic field is created with the uniformly charged endless plate and sphere. The surface charge density of the plate is σ 1. The radius of sphere is R, the surface charge density of the sphere is σ 2. The sphere centre is situated at a distance of l from the plane. Find the electric intensity at the point, which is situated between the sphere and the plate at a distance of r 1 from the plate.
TABLE OF TASK VARIANTS
Table 1.1
| Variant | Problem statement number | Q 1, nC | Q 2, nC | τ 1, nC /m | τ 2, nC /m | σ 1, nC /m 2 | σ 2, nC /m 2 | R, cm | l, cm | r 1, cm | r 2, cm |
| 1а | +0.2 | – | – | – | +2 | +4 | – | – | – | – | |
| 2а | –3 | +6 | – | – | – | – | – | ||||
| – | – | –6 | –9 | – | – | – | |||||
| – | – | – | – | +10 | +40 | – | |||||
| – | – | –2 | +3 | – | – | – | |||||
| 1б | +0.2 | – | – | – | –2 | –3 | – | – | – | – | |
| 2б | +0.2 | – | – | – | – | +3 | – | ||||
| – | – | +3 | +4 | – | – | – | |||||
| – | – | – | – | –4 | –9 | – | |||||
| 1а | +0.1 | – | – | – | +2 | –3 | – | – | – | – | |
| 2б | +0.1 | – | – | – | – | –10 | – | ||||
| – | – | +1 | +2 | – | – | – | |||||
| 1б | +0.4 | – | – | – | –5 | +3 | – | – | – | – | |
| 2а | +1 | +5 | – | – | – | – | – | ||||
| – | – | +10 | –5 | – | – | – | |||||
| – | – | – | – | –6 | +8 | – | |||||
| – | – | –40 | –30 | – | – | – | |||||
| 1а | +0.3 | – | – | – | –4 | –1 | – | – | – | – | |
| 2а | –2 | –4 | – | – | – | – | – | ||||
| – | – | +8 | +4 | – | – | – | |||||
| – | – | – | – | +4 | –6 | – | |||||
| – | – | –3 | –4 | – | – | – | |||||
| 1б | +0.1 | – | – | – | +3 | +1 | – | – | – | – | |
| 2б | –0.4 | – | – | – | – | –8 | – | ||||
| – | – | –8 | +6 | – | – | – | |||||
| 1а | –0.4 | – | – | – | –2 | +4 | – | – | – | – | |
| – | – | +2 | –4 | – | – | ||||||
| 2б | –0.5 | – | – | – | – | +9 | – | ||||
| – | – | – | – | –3 | –8 | – | |||||
| – | – | +4 | +6 | – | – | – |
Problem 1.5.
DIRECT CURRENT
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