| № |
Condition |
free/or 0.5$ |
| 641 | The space between two large parallel plates separated by a distance L = 5.0 mm is filled with helium under a pressure p = 1.0 Pa. One plate is kept at a temperature t1 = 17 °C and the other, at a temperature t2 =37 °C. Find the mean free path of helium atoms and the heat flow density. |
|
| 642 | Find the temperature distribution in the space between two coaxial cylinders of radii R1 a nd R2 filled with a uniform heat conducting substance if the temperatures of the cylinders are constant and are equal to T1 and T2 respectively. |
|
| 643 | Solve the foregoing problem for the case of two concentric spheres of radii. R1 and R2 and temperatures T1 and T2. |
|
| 644 | A constant electric current flows along a uniform wire with cross-sectional radius R and heat conductivity coefficient x. A unit volume of the wire generates a thermal power w. Find the temperature distribution across the wire provided the steady-state temperature at the wire surface is equal to T0. |
|
| 645 | The thermal power of density w is generated uniformly inside a uniform sphere of radius R and heat conductivity coefficient x. Find the temperature distribution in the sphere provided the steady-state temperature at its surface is equal to T0. |
|
| 646 | Calculate the ratio of the electrostatic to gravitational interaction forces between two electrons, between two protons. At what value of the specific charge q/m of a particle would these forces become equal (in their absolute values) in the case of interaction of identical particles? |
|
| 647 | What would be the interaction force between two copper spheres, each of mass 1 g, separated by the distance 1 m, if the total electronic charge in them differed from the total charge of the nuclei by one per cent? |
|
| 648 | Two small equally charged spheres, each of mass m, are suspended from the same point by silk threads of length l. The distance between the spheres x << l. Find the rate dq/dt with which the charge leaks off each sphere if their approach velocity varies as v = a/sqrt(x), where a is a constant. |
|
| 649 | Two positive charges q1 and q2 are located at the points with radius vectors r1 and r2. Find a negative charge q3 and a radius vector r3 of the point at which it has to be placed for the force acting on each of the three charges to be equal to zero. |
|
| 650 | A thin wire ring of radius r has an electric charge q. What will be the increment of the force stretching the wire if a point charge q0 is placed at the ring's centre? |
|
| 651 | A positive point charge 50 μC is located in the plane xy at the point with radius vector r0 = 2i + 3j, where i and j are the unit vectors of the x and y axes. Find the vector of the electric field strength E and its magnitude at the point with radius vector r = 8i - 5j. Here r0 and r are expressed in metres. |
|
| 652 | Point charges q and -q are located at the vertices of a square with diagonals 2l as shown in Fig. 3.1. Find the magnitude of the electric field strength at a point located symmetrically with respect to the vertices of the square at a distance x from its centre. |
|
| 653 | A thin half-ring of radius R = 20 cm is uniformly charged with a total charge q = 0.70 nC. Find the magnitude of the electric field strength at the curvature centre of this half-ring. |
|
| 654 | A thin wire ring of radius r carries a charge q. Find the magnitude of the electric field strength on the axis of the ring as a function of distance l from its centre. Investigate the obtained function at l >> r. Find the maximum strength magnitude and the corresponding distance l. Draw the approximate plot of the function E(l). |
|
| 655 | A point charge q is located at the centre of a thin ring of radius R with uniformly distributed charge -q. Find the magnitude of the electric field strength vector at the point lying on the axis of the ring at a distance x from its centre, if x >> R. |
|
| 656 | A system consists of a thin charged wire ring of radius R and a very long uniformly charged thread oriented along the axis of the ring, with one of its ends coinciding with the centre of the ring. The total charge of the ring is equal to q. The charge of the thread (per unit length) is equal to λ. Find the interaction force between the ring and the thread. |
|
| 657 | A thin nonconducting ring of radius R has a linear charge density λ = λ0 cos φ, where λ0 is a constant, φ is the azimuthal angle. Find the magnitude of the electric field strength (a) at the centre of the ring; (b) on the axis of the ring as a function of the distance x from its centre. Investigate the obtained function at x >> R. |
|
| 658 | A thin straight rod of length 2a carrying a uniformly distributed charge q is located in vacuum. Find the magnitude of the electric field strength as a function of the distance r from the rod's centre along the straight line (a) perpendicular to the rod and passing through its centre; (b) coinciding with the rod's direction (at the points lying outside the rod). Investigate the obtained expressions at r >> a. |
|
| 659 | A very long straight uniformly charged thread carries a charge λ per unit length. Find the magnitude and direction of the electric field strength at a point which is at a distance y from the thread and lies on the perpendicular passing through one of the thread's ends. |
|
| 660 | A thread carrying a uniform charge λ per unit length has the configurations shown in Fig. 3.2 a and b. Assuming a curvature radius R to be considerably less than the length of the thread, find the magnitude of the electric field strength at the point O. |
|
