1. How does a Van de Graaff Generator work? What is the magnitude of the electric field inside the dome of a charged Van de Graaff generator?
2. How does the charge on one plate of a capacitor compare with that on the opposite plate?
3. How does a capacitor stores energy?
1. A Van de Graaff Generator is a device that uses a moving belt to create a large difference in electric potential between its dome and base. Here's a step-by-step explanation of how it works:
Step 1: The Van de Graaff Generator consists of a large metal dome and a motor-driven rubber belt. The belt is made of a non-conductive material.
Step 2: The belt is driven by a motor and moves continuously. As the belt moves, it rubs against two rollers - one at the bottom and one near the top.
Step 3: The bottom roller is made of metal and is connected to the ground. When the belt rubs against the bottom roller, it becomes negatively charged due to the transfer of electrons from the belt to the roller.
Step 4: As the belt continues to move, it carries the negative charge up towards the top roller. The top roller is located near the metal dome of the Van de Graaff Generator.
Step 5: As the belt rubs against the top roller, some of the negative charge is transferred to the dome. This process continues, with more negative charge being transferred to the dome as the belt continues to move.
Step 6: Since the dome is isolated and not connected to the ground, it accumulates a large amount of negative charge.
The magnitude of the electric field inside the dome of a charged Van de Graaff generator can be quite high. It depends on the charge on the dome and the radius of the dome. The electric field can be calculated using the formula: Electric Field = Charge / (4πε₀r²), where ε₀ is the vacuum permittivity and r is the radius of the dome.
2. The charge on one plate of a capacitor is equal in magnitude but opposite in sign to the charge on the opposite plate. This is due to the principle of charge conservation. When the capacitor is connected to a power source, electrons flow from the negative terminal of the source and onto one plate of the capacitor, giving it a negative charge. At the same time, an equal amount of positive charge is induced on the other plate, creating an electric field between the plates. The charge on the plates is equal in magnitude but opposite in sign.
3. A capacitor stores energy in an electric field. Here's a step-by-step explanation of how it works:
Step 1: A capacitor consists of two conducting plates separated by a dielectric material or a vacuum. The plates are connected to a power source or a battery.
Step 2: When a voltage is applied across the plates, electrons flow from the negative terminal of the power source and accumulate on one plate, while an equal number of electrons are repelled and flow to the positive terminal, leaving the other plate with a positive charge.
Step 3: The accumulation of opposite charges on the plates creates an electric field between them.
Step 4: The energy is stored in the electric field between the plates. The amount of energy stored in a capacitor can be calculated using the formula: Energy (E) = 1/2 * C * V², where C is the capacitance of the capacitor and V is the voltage applied across the plates.
Step 5: When the capacitor is disconnected from the power source, it can release this stored energy to perform work, such as powering a circuit or discharging a flash in a camera.
Overall, a capacitor stores energy by accumulating opposite charges on its plates, which creates an electric field between them.
1. A Van de Graaff generator works by accumulating and distributing static electricity. It consists of a large metal dome and a rubber belt that moves over two pulleys. Initially, the belt is neutral and as it moves, it rubs against a roller at the base of the generator, which transfers electrons from the roller to the belt. The moving belt then carries the electrons to the dome, where they accumulate on the surface. This continuous transfer of electrons from the roller to the belt creates a large buildup of static charge on the dome.
The magnitude of the electric field inside the dome of a charged Van de Graaff generator can be calculated using the equation E = kQ/r^2, where E is the electric field, k is the Coulomb's constant (~9 x 10^9 Nm^2/C^2), Q is the charge on the dome, and r is the radius of the dome. The charge on the dome depends on the amount of excess electrons that have accumulated. The larger the accumulation of charge, the stronger the electric field will be inside the dome.
2. In a capacitor, the charge on one plate is equal in magnitude and opposite in sign to the charge on the opposite plate. When a voltage is applied across the capacitor plates, electrons accumulate on one plate, giving it a negative charge, and an equal number of electrons are pulled away from the other plate, giving it a positive charge. This separation of charges creates an electric field between the plates and allows the capacitor to store charge.
The charge on each plate of a capacitor can be calculated using the equation Q = CV, where Q is the charge, C is the capacitance of the capacitor, and V is the voltage applied across the plates. The capacitance value determines how much charge can be stored on each plate for a given voltage.
3. A capacitor stores energy in its electric field. When a voltage is applied across the plates of the capacitor, work is done to move the charges. The energy stored in a capacitor can be calculated using the equation E = 1/2CV^2, where E is the energy, C is the capacitance, and V is the voltage across the plates.
The energy storage capacity of a capacitor depends on its capacitance value and the square of the voltage applied. The higher the capacitance, the more charge can be stored, and the higher the voltage, the more energy can be stored. Capacitors are commonly used in electronic circuits to store energy and provide power when needed, such as in flash photography or smoothing out voltage fluctuations.