Question

Работа по перемещению заряда. из точки A в точку B составляет 3 Дж. Расстояние между данными точками = 50мм,а велечина перемещаемого заряда = 6 мкКл. Определите напряжённость данного электростатического поля Какой заряд должна иметь пылинка массой 100 мкг, чтобы она "висела" в направленном вверх электростатическом поле напряжённостью 23 кН/Кл?

Answer 1

Ответ:

1)

A=qEd

E=A/qd

E=3/0.05*6*10^-6=10^7=10 000 000 H/Кл

2)

q - ?

mg=E*q

q=mg/E

q=100 * 10^-6 * 10 / 23*10^3=10^-6/23≈4.347 * 10^-8 Кл

Answer 2

Calculation of Electric Field Intensity

To determine the electric field intensity between points A and B, we can use the formula:

Electric field intensity (E) = Work done (W) / Charge (Q)

Given that the work done (W) is 3 J and the charge (Q) is 6 μC, we can substitute these values into the formula to find the electric field intensity.

E = 3 J / 6 μC

Before proceeding with the calculation, we need to convert the charge from microcoulombs (μC) to coulombs (C) to ensure consistent units.

1 μC = 1 × 10^-6 C

Therefore, the charge (Q) is 6 × 10^-6 C.

Now we can calculate the electric field intensity:

E = 3 J / (6 × 10^-6 C)

Simplifying the expression:

E = 3 × 10^6 J/C

Thus, the electric field intensity between points A and B is 3 × 10^6 J/C.

Calculation of Charge for Dust Particle

To determine the charge required for a dust particle to "hang" in an upward-directed electric field with an intensity of 23 kN/C, we can use the formula:

Electric field intensity (E) = Force (F) / Charge (Q)

Given that the electric field intensity (E) is 23 kN/C and the mass of the dust particle is 100 μg, we need to find the force (F) acting on the particle.

The force acting on the dust particle can be calculated using Newton's second law:

Force (F) = Mass (m) × Acceleration (a)

The acceleration experienced by the dust particle in the electric field is equal to the gravitational acceleration (g) because the particle is in equilibrium. The gravitational acceleration is approximately 9.8 m/s^2.

Force (F) = Mass (m) × Gravitational acceleration (g)

Converting the mass from micrograms (μg) to kilograms (kg):

1 μg = 1 × 10^-9 kg

Therefore, the mass (m) is 100 × 10^-9 kg.

Substituting the values into the formula:

Force (F) = (100 × 10^-9 kg) × (9.8 m/s^2)

Simplifying the expression:

Force (F) = 9.8 × 10^-7 N

Now we can calculate the charge (Q) required for the dust particle:

23 kN/C = (9.8 × 10^-7 N) / Charge (Q)

Rearranging the formula:

Charge (Q) = (9.8 × 10^-7 N) / (23 × 10^3 N/C)

Simplifying the expression:

Charge (Q) = 9.8 × 10^-7 / 23 × 10^3 C

Thus, the charge required for the dust particle to "hang" in the upward-directed electric field with an intensity of 23 kN/C is approximately 4.26 × 10^-11 C.