Question

Электрическое поле образовано бесконечной плоскостью, заряженной с поверхностной плоскостью 1,40 мкКЛ/м2 и двумя точечными зарядами (20,0 и -40,0 нКл). Заряды расположены на одной прямой, параллельной плоскости, на расстоянии 160 мм друг от друга. Найти значение и направление напряженности электрического поля в середине этого расстояния.

Answer 1

У меня на странице (вконтакт) есть конспект-сводка формул школьного курса. Возьмите формулу 3.1.5 для напряженности поля точечного заря и формулу   3.1.22 для поля заряженной плоскости и сложите три вектора напряженности, т.е. примените принцип суперпозиции полей 3.1.7
Г.И. Левиев

Answer 2

Calculation of Electric Field Intensity

To find the value and direction of the electric field intensity at the midpoint between the two charges, we can use the principle of superposition. The electric field intensity at a point due to multiple charges is the vector sum of the electric field intensities produced by each individual charge.

Let's denote the positive charge as q1 = 20.0 nC and the negative charge as q2 = -40.0 nC. The charges are located on a straight line parallel to the surface of the infinite plane, at a distance of 160 mm (0.16 m) from each other.

The electric field intensity at the midpoint between the charges can be calculated using the formula:

E = (k * q1) / r1^2 + (k * q2) / r2^2

Where: - E is the electric field intensity - k is the electrostatic constant (k = 9 * 10^9 Nm^2/C^2) - q1 and q2 are the magnitudes of the charges - r1 and r2 are the distances from the midpoint to each charge

Let's calculate the electric field intensity step by step:

1. Calculate the distance from the midpoint to each charge: - r1 = 0.08 m (half the distance between the charges) - r2 = 0.08 m (half the distance between the charges)

2. Substitute the values into the formula: - E = (9 * 10^9 Nm^2/C^2 * 20.0 * 10^-9 C) / (0.08 m)^2 + (9 * 10^9 Nm^2/C^2 * -40.0 * 10^-9 C) / (0.08 m)^2

3. Simplify the equation: - E = (9 * 10^9 Nm^2/C^2 * 20.0 * 10^-9 C - 9 * 10^9 Nm^2/C^2 * 40.0 * 10^-9 C) / (0.08 m)^2

4. Calculate the numerator: - E = (9 * 10^9 Nm^2/C^2 * (20.0 - 40.0) * 10^-9 C) / (0.08 m)^2

5. Simplify the numerator: - E = (9 * 10^9 Nm^2/C^2 * -20.0 * 10^-9 C) / (0.08 m)^2

6. Calculate the denominator: - E = (9 * 10^9 Nm^2/C^2 * -20.0 * 10^-9 C) / 0.0064 m^2

7. Simplify the denominator: - E = - (9 * 10^9 Nm^2/C^2 * 20.0 * 10^-9 C) / 0.0064 m^2

8. Calculate the final result: - E = - 281.25 N/C

Therefore, the value of the electric field intensity at the midpoint between the charges is 281.25 N/C. The negative sign indicates that the electric field is directed towards the negative charge.