# Induced Charge on a Conducting Disk

• cardsfan527
In summary, the problem involves a large, charged disk with a radius of 1.1 meters and a uniformly distributed charge of -7e–5 C. A circular piece of aluminum foil with a radius of 6 cm and a thickness of 1 mm is placed 3 mm away from the disk, parallel to it. The net electric field at the center of the foil is 0, as a conductor will not have an electric field inside of it. To calculate the magnitude of the charge on the left circular face of the foil, the method of images can be used, considering the induced surface charge density and integrating over the surface.
cardsfan527

## Homework Statement

A large, thin plastic disk with radius R = 1.1 meter carries a uniformly distributed charge of Q = -7e–5 C. A circular piece of aluminum foil is placed d = 3 mm from the disk, parallel to the disk. The foil has a radius of r = 6 cm and a thickness t = 1 millimeter.

a. Find the net electric field at the center of the foil.
b. Calculate the magnitude q of the charge on the left circular face of the foil.

## Homework Equations

E = 1/(4*∏*ε)*q/r^2

## The Attempt at a Solution

I know that the answer to part (a) is 0, because a conductor will not have an electric field inside of it.

I also know that the charge on one side of the foil disk will be equal and opposite to the charge on the other side, since the disk has a neutral total charge. I'm just unsure of exactly where to go from there. Should I use force equations, since I know that the charges are at rest? Or is there something I know about the electric field that I can use?

Hi.
So you have a zero field inside the conductor, and non-zero right outside. Determine the field outside, remember the formula for induced surface charge density, then integrate over the surface...

Thanks, Goddar. I guess my problem is calculating the electric field. Could you send me in the right direction?

Method of images, since the disk is "large"...

I would approach this problem by first considering the properties of conductors and how they interact with electric fields. Conductors are materials that allow charges to move freely, which means that any excess charge placed on the surface of a conductor will distribute itself evenly throughout the surface in order to minimize the repulsion between like charges.

In this case, the plastic disk is a conductor and has a uniform charge distribution, meaning that the charge is evenly spread out over the entire surface. When the aluminum foil is placed near the disk, it will experience a repulsive force from the induced charges on the disk surface. However, since the foil is also a conductor, it will also distribute this induced charge evenly over its surface.

Therefore, the net electric field at the center of the foil will be 0, as you correctly stated. This is because the electric field from the induced charges on the disk will be cancelled out by the induced charges on the foil.

To calculate the magnitude of the charge on the left circular face of the foil, we can use the equation you provided, E = 1/(4*∏*ε)*q/r^2. Since the electric field at the center of the foil is 0, we can rearrange this equation to solve for q:

q = 0 * 4*∏*ε*r^2 = 0

This means that the charge on the left circular face of the foil is 0. However, this does not mean that there is no charge on the foil at all. There will still be an induced charge on the foil, but it will be evenly distributed over the entire surface and cancel out any external electric field.

In conclusion, the net electric field at the center of the foil is 0 and the charge on the left circular face of the foil is 0. This is due to the properties of conductors and how they interact with electric fields.

## 1. What is induced charge on a conducting disk?

Induced charge on a conducting disk refers to the redistribution of electric charge on the surface of a disk when it is placed in an external electric field. This redistribution of charge creates an electric field within the disk that is opposite in direction to the external field.

## 2. How is induced charge on a conducting disk different from static charge?

Induced charge on a conducting disk is a temporary redistribution of charge, while static charge is a permanent buildup of charge. Induced charge only occurs when the disk is in an external electric field, whereas static charge can exist without the presence of an external field.

## 3. What factors affect the amount of induced charge on a conducting disk?

The amount of induced charge on a conducting disk depends on the strength of the external electric field, the size and shape of the disk, and the conductivity of the material the disk is made of. Higher electric field strength, larger disk size, and higher conductivity all result in a greater amount of induced charge.

## 4. How is induced charge on a conducting disk related to capacitance?

Induced charge on a conducting disk is directly related to capacitance. The greater the amount of induced charge, the greater the capacitance of the disk. This is because the induced charge creates an electric field within the disk, which is a key component of capacitance.

## 5. Can induced charge on a conducting disk be used for practical applications?

Yes, induced charge on a conducting disk has practical applications in devices such as capacitors, sensors, and antennas. By controlling the amount and distribution of induced charge on a conducting disk, these devices can perform various functions such as storing electrical energy, detecting changes in electric fields, and transmitting and receiving electromagnetic waves.

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