Question

Помогите пжлста срочняк просто... Электрон с энергией Wk = 6,4*10-17 Дж (в бесконечности) движется вдоль линии напряженности по направлению к поверхности металлической заряженной сферы радиусом R =10 см. Определить минимальное расстояние rmin , на которое приблизится электрон к поверхности сферы, если её заряд Q = –10 нКл.

Answer 1

Шмаовичрчррчрчиичсвмамвиив

Answer 2

Calculation of the Minimum Distance an Electron Approaches a Charged Sphere

To determine the minimum distance an electron approaches the surface of a charged sphere, we can use the given information about the electron's energy and the sphere's properties.

The energy of the electron, Wk, is given as 6.4 * 10^(-17) J. The sphere has a radius, R, of 10 cm, and a charge, Q, of -10 nC.

To find the minimum distance, rmin, we can use the equation for the electric potential energy of a charged particle near a charged sphere:

Wk = q * V

where Wk is the kinetic energy of the electron, q is the charge of the electron, and V is the electric potential at the surface of the sphere.

The electric potential at the surface of a charged sphere is given by:

V = k * Q / R

where k is the Coulomb constant (approximately 9 * 10^9 Nm^2/C^2), Q is the charge of the sphere, and R is the radius of the sphere.

Substituting the values into the equation, we have:

6.4 * 10^(-17) J = q * (k * Q / R)

To find the charge of the electron, q, we can rearrange the equation:

q = (6.4 * 10^(-17) J) / (k * Q / R)

Now we can substitute the given values into the equation:

q = (6.4 * 10^(-17) J) / (9 * 10^9 Nm^2/C^2 * (-10 * 10^(-9) C) / (0.1 m))

Simplifying the equation, we get:

q = -0.071 mC

Now that we have the charge of the electron, we can find the minimum distance, rmin, using the equation for the electric potential at a distance r from the center of the sphere:

V = k * Q / r

Rearranging the equation, we have:

r = k * Q / V

Substituting the values into the equation, we get:

rmin = (9 * 10^9 Nm^2/C^2 * (-10 * 10^(-9) C)) / (6.4 * 10^(-17) J / (0.1 m))

Simplifying the equation, we find:

rmin = -1.40625 m

Therefore, the minimum distance, rmin, at which the electron approaches the surface of the charged sphere is approximately -1.40625 meters.

Please note that the negative sign indicates that the electron approaches the surface from the inside of the sphere.