Electric Charge Distribution in Cylindrical Capacitors

In summary, a potential difference of 160V is applied to two col-linear conducting cylinders with radii of 15 cm and 10 cm and a height of 38 cm. The charge applied to each cylinder can be calculated using the formula Q = Vε0A/d, resulting in a value of 1.69*10^-10 C. However, this formula is for parallel plate capacitors and may not apply to cylindrical capacitors.
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Homework Statement


A potential difference of 160V is applied across two col-linear conducting cylinders. the radius of the outer cylinder is 15 cm, the radius of the inner cylinder is 10 cm, the height of the two cylinders is 38 cm.
a. How much charge is applied to each of the cylinders?
b. What is the magnitude of the electric field between the two cylinders? (magnitudes inside inner and outer cylinder)


Homework Equations



V = Ed = Qd/ε0A


The Attempt at a Solution



a.
V = Qd/ε0A
Q = Vε0A/d = [Vε0(2pi(r1 - r2)^2*h] / d ///(d and one of the (r1 - r2)^2 cancel)
Q = (160)(8.85*10^-12)(2pi)(0.05)(0.38) = 1.69*10^-10 C.
The answer is supposed to be 8.34 *10^-9 C.
 
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FAQ: Electric Charge Distribution in Cylindrical Capacitors

What is the concept of charge applied to cylinders?

The concept of charge applied to cylinders refers to the process of introducing electric charge to a cylindrical object, such as a wire or a capacitor. This charge can either be positive or negative and can be used to create an electric field or potential difference within the cylinder.

How is charge applied to cylinders calculated?

The calculation of charge applied to cylinders depends on the type of cylinder and the amount of charge being applied. For a wire, the charge is typically calculated using the formula Q=CV, where Q is the charge, C is the capacitance of the wire, and V is the potential difference across the wire. For a capacitor, the charge is calculated using the formula Q=CV, where Q is the charge, C is the capacitance of the capacitor, and V is the potential difference across the capacitor.

What are some real-world applications of charge applied to cylinders?

Charge applied to cylinders has many practical applications in everyday life. One common example is the use of capacitors in electronic devices, such as cell phones and computers, to store and release electrical charge. Another example is the use of wires to carry electricity in power lines and circuits. Additionally, charge applied to cylinders is used in scientific research, such as in particle accelerators, to manipulate and study charged particles.

What happens when too much charge is applied to a cylinder?

When an excessive amount of charge is applied to a cylinder, it can lead to a phenomenon known as electric breakdown. This occurs when the electric field within the cylinder becomes too strong and can cause the cylinder to lose its insulating properties. This can result in a discharge of electrical energy, which can be dangerous and cause damage to the cylinder or surrounding objects.

How does charge applied to cylinders affect the behavior of charged particles?

The introduction of charge to a cylinder can have a significant impact on the behavior of charged particles. For example, a negatively charged cylinder can attract positively charged particles, while a positively charged cylinder can repel them. Additionally, the strength of the electric field within the cylinder can affect the speed and trajectory of charged particles passing through it. This is why charge applied to cylinders is essential in controlling and manipulating charged particles in various scientific experiments.

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