Question

Маленький шарик массой 5 г висит на упругой нити. Коэффициент упругости нити составляет 125 Н/м. Шарик зарядили до 8 нКл и поместили в вертикальный плоский воздушный конденсатор расстояние между обкладками которого равно 4 см. Найдите разность потенциалов между обкладками конденсатора, если нить растянулась на 0,4 мм. Ускорение свободного падения принять равным 10 м/с2.

Answer 1

Дано
m=5г=5*10^(-3)кг
k=125 H/м
q=8нКл=8*10^(-9)Кл
d=4см=4*10^(-2)м
l=0,4мм=4*10^(-4)м
g=10 м/с²=10 H/кг
Найти U
для плоского конденсатора
U= Ed, где Е напряжнность эл. поля, d - расстояние межу обкладками.
Сила тяжести, действующая на шарик mg. Она тянет шарик вниз.
сила, действующая на шарик со стороны электрического поля Eq, она отклоняет шарик в сторону.
(mg)²+(Eq)²=(kl)²
E²q²=(kl)²-(mg)²
E=√( (kl)²-(mg)²)/q
U=(d/q) √( (kl)²-(mg)²)= ( 4*10^(-2)м/ 8*10^(-9)Кл)√( 125² H²/м²* 4²*10^(-8)м² - 5²*10^(-6)кг² 10²H²/кг²))= 5*10^6 м/Кл √(25*10^(-4) H²-25*10(-4)Н²)=0В
Ответ: конденсатор не заражен

Answer 2

Calculation of Potential Difference in the Capacitor

To find the potential difference between the plates of the capacitor, we need to consider the gravitational force acting on the mass of the ball and the electrostatic force acting on the charged ball.

The gravitational force can be calculated using the formula:

F_gravity = m * g

where: - F_gravity is the gravitational force, - m is the mass of the ball (given as 5 g, which is equal to 0.005 kg), - g is the acceleration due to gravity (given as 10 m/s^2).

Substituting the given values, we have:

F_gravity = 0.005 kg * 10 m/s^2 = 0.05 N.

The electrostatic force can be calculated using the formula:

F_electrostatic = q * E

where: - F_electrostatic is the electrostatic force, - q is the charge on the ball (given as 8 nC, which is equal to 8 * 10^-9 C), - E is the electric field between the plates of the capacitor.

To find the electric field, we can use the formula:

E = V / d

where: - E is the electric field, - V is the potential difference between the plates of the capacitor (which we need to find), - d is the distance between the plates of the capacitor (given as 4 cm, which is equal to 0.04 m).

Substituting the given values, we have:

E = V / 0.04 m

Rearranging the formula, we get:

V = E * 0.04 m

Now, we need to find the electric field. The electric field can be calculated using the formula:

E = k * q / r^2

where: - E is the electric field, - k is the electrostatic constant (given as 9 * 10^9 Nm^2/C^2), - q is the charge on the ball (given as 8 nC, which is equal to 8 * 10^-9 C), - r is the distance between the ball and the center of the capacitor plates.

The distance r can be calculated by subtracting the elongation of the string from the original length of the string. The elongation of the string can be calculated using Hooke's Law:

F_spring = k_spring * x

where: - F_spring is the spring force, - k_spring is the spring constant (given as 125 N/m), - x is the elongation of the string (given as 0.4 mm, which is equal to 0.0004 m).

Substituting the given values, we have:

F_spring = 125 N/m * 0.0004 m = 0.05 N

Since the spring force is equal to the gravitational force, we can equate the two:

F_spring = F_gravity

0.05 N = 0.05 N

Now, we can calculate the electric field:

E = k * q / r^2

E = (9 * 10^9 Nm^2/C^2) * (8 * 10^-9 C) / (0.05 m)^2

Simplifying the equation, we get:

E = 1152 N/C

Substituting this value into the equation for potential difference, we have:

V = (1152 N/C) * (0.04 m)

Calculating the value, we find:

V = 46.08 V

Therefore, the potential difference between the plates of the capacitor is 46.08 V.