a small conducted sphere is attached to the end of an insulating rod .it carries a charge of +5.0*10-9 C. the plates ,which are 4.0 cm apart, are connected to a 50 000 V supply.
What plates? Is there a question here?
and the question is...
To find the potential difference between the plates and the electric field created by the plates, we can follow these steps:
Step 1: Calculate the potential difference (voltage) between the plates.
The formula to calculate the potential difference between two plates is:
V = Ed, where V is the voltage, E is the electric field, and d is the distance between the plates.
Since the plates are connected to a 50,000 V supply, the potential difference between the plates is 50,000 V.
Step 2: Calculate the electric field between the plates.
The formula to calculate the electric field between two plates is:
E = V/d, where E is the electric field, V is the voltage, and d is the distance between the plates.
In this case, the voltage is 50,000 V, and the distance between the plates is 4.0 cm (or 0.04 m). Plugging these values into the formula:
E = 50,000 V / 0.04 m = 1,250,000 V/m.
Step 3: Determine the force on the sphere.
The force on a charged object in an electric field can be calculated using the formula:
F = qE, where F is the force, q is the charge, and E is the electric field.
In this case, the charge on the sphere is +5.0 * 10^-9 C, and the electric field is 1,250,000 V/m. Plugging these values into the formula:
F = (5.0 * 10^-9 C) * (1,250,000 V/m) = 6.25 * 10^-3 N.
Therefore, the potential difference between the plates is 50,000 V, the electric field created by the plates is 1,250,000 V/m, and the force on the sphere is 6.25 * 10^-3 N.
To analyze the given situation, let's break down the information step by step:
1. A small conducted sphere is attached to the end of an insulating rod.
2. The small sphere carries a positive charge of +5.0 × 10^-9 C.
3. The plates are 4.0 cm apart.
4. The plates are connected to a 50,000 V supply.
Now, let's use this information to find out more about the electric field, potential difference, and potential energy in this system:
1. Electric Field (E):
The electric field between the plates can be calculated using the formula:
E = V / d
Where,
E = Electric field (in N/C)
V = Potential difference between the plates (in volts)
d = Distance between the plates (in meters)
Since the distance is given in centimeters, we need to convert it to meters by dividing it by 100.
d = 4.0 cm = 4.0/100 m = 0.04 m
Now, we can substitute the values:
E = 50,000 V / 0.04 m = 1,250,000 V/m
Therefore, the electric field between the plates is 1,250,000 V/m.
2. Potential Difference (V):
The potential difference between the plates is given as 50,000 V.
3. Potential Energy (PE):
The potential energy of the charged sphere in the electric field can be calculated using the formula:
PE = q * V
Where,
PE = Potential energy (in joules)
q = Charge (in coulombs)
V = Potential difference (in volts)
Substituting the values:
PE = (5.0 × 10^-9 C) * (50,000 V) = 2.5 × 10^-4 J
Therefore, the potential energy of the charged sphere is 2.5 × 10^-4 joules.
Please note that in this explanation, we have used the given information and applied relevant formulas to find the answers.