Individual tasks for problem 1.1. The principle of superposition of electric fields

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 σ₁ and σ₂. Find force, which acts in this field on the point charge Q₁ , if it’s situated:

а) between the planes;

b) outside of planes.

2 The point charge Q₁ 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 r₁ and r₂, if:

а) the charge of sphere equals Q₂ ;

b) surface density of the sphere charge equals σ₂.

3 The long thread, uniformly charged with the linear density τ₁, 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 τ₂. Define the electrostatic field intensity in the other points:

1) at a distance of r₁ 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 τ₁ and τ₂. The distance between the thread is l. Define the electrostatic field intensity at the point, which is situated at a distance of r₁ from the first thread and r₂ 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 σ₁. The radius of sphere is R, the surface charge density of the sphere is σ₂. 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 r₁ from the plate.

Table of task variants

Table 1.1

Variant	Problem statement number	Q1 , nC	Q2 , nC	τ1 , nC /m	τ2 , nC /m	σ1 , nC /m^2	σ2 , nC /m^2	R , cm	l , cm	r1 , cm	r2 , cm
1	1а	+0.2	–	–	–	+2	+4	–	–	–	–
2	2а	–3	+6	–	–	–	–	6	–	3	10
3	4	–	–	–6	–9	–	–	–	6	6	6
4	5	–	–	–	–	+10	+40	4	10	2	–
5	3	–	–	–2	+3	–	–	5	5	4	–
6	1б	+0.2	–	–	–	–2	–3	–	–	–	–
7	2б	+0.2	–	–	–	–	+3	10	–	1	20
8	4	–	–	+3	+4	–	–	–	5	3	4
9	5	–	–	–	–	–4	–9	6	12	3	–
10	1а	+0.1	–	–	–	+2	–3	–	–	–	–
11	2б	+0.1	–	–	–	–	–10	5	–	3	10
12	3	–	–	+1	+2	–	–	4	5	1	–
13	1б	+0.4	–	–	–	–5	+3	–	–	–	–
14	2а	+1	+5	–	–	–	–	8	–	5	10
15	4	–	–	+10	–5	–	–	–	10	10	10
16	5	–	–	–	–	–6	+8	2	5	1	–
17	4	–	–	–40	–30	–	–	–	5	4	3
18	1а	+0.3	–	–	–	–4	–1	–	–	–	–
19	2а	–2	–4	–	–	–	–	5	–	2	6
20	4	–	–	+8	+4	–	–	–	8	8	8
21	5	–	–	–	–	+4	–6	5	10	4	–
22	3	–	–	–3	–4	–	–	6	3	3	–
23	1б	+0.1	–	–	–	+3	+1	–	–	–	–
24	2б	–0.4	–	–	–	–	–8	8	–	5	10
25	4	–	–	–8	+6	–	–	–	5	4	3
26	1а	–0.4	–	–	–	–2	+4	–	–	–	–
27	3	–	–	+2	–4	–	–	7	5	4
28	2б	–0.5	–	–	–	–	+9	10	–	5	15
29	5	–	–	–	–	–3	–8	4	18	6	–
30	4	–	–	+4	+6	–	–	–	10	4	6