An airplane is flying through a thundercloud at a height of 2000 m . (This is a very dangerous t

An airplane is flying through a thundercloud at a height of...

An airplane is flying through a thundercloud at a height of 2000 $\mathrm{m}$ . (This is a very dangerous thing to do because of updrafts, turbulence, and the possibility of electric discharge.) If a charge concentration of $+40.0 \mathrm{C}$ is above the plane at a height of 3000 $\mathrm{m}$ within the cloud and a charge concentration of $-40.0 \mathrm{C}$ is at height $1000 \mathrm{m},$ what is the electric field at the aircraft?

Key Concepts

Sign of Charges and Field Direction

The sign of a charge determines the direction of the electric field it produces. Positive charges create electric fields that emanate outward, while negative charges produce fields that point inward. This directional property is vital when combining fields from multiple charges to determine the overall field direction at a given point.

Superposition Principle

The superposition principle asserts that when multiple sources contribute to an electric field, the net electric field at any point is the vector sum of the individual electric fields produced by each source. This principle enables the analysis of complex charge configurations by considering the effect of each charge independently.

Distance Dependence in Electric Fields

The effect of a charge on the electric field diminishes with increasing distance, following an inverse square law. This means that as the distance from a charge increases, the electric field strength decreases rapidly, which is crucial when considering contributions from charges at different locations.

Electric Field

The electric field is a vector field that represents the force per unit charge exerted on a test charge at any point in space. It characterizes both the magnitude and direction of the force that would act on a positive test charge placed in the field, and it is fundamental in understanding electric interactions in a system.

Coulomb's Law

Coulomb's law quantifies the electric force between two point charges. It states that the force between the charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This principle is essential for calculating the electric field generated by a discrete charge distribution.

Transcript

00:01 So in this problem, we basically have an airplane that is flying between two clouds that are charged.

00:08 So these charged clouds have different charges corresponding to them.

00:17 So the concentration for the higher cloud, which is, first we have the head of the plane.

00:26 So this is from the ground, we have this, for example, you can say this is h1, then we have a head.

00:36 2 which is from the ground age 3 and we have 138 which is from the ground age 3.

00:49 Of course the concentration charge concentrations for every cloud are for the higher cloud is positive 40 columns and for the lower cloud it is negative 40 columns so total charge differences 80 columns and basically this airplane here is like between condensator plates and to find the total electric wheel that is acting on the plane we need two components on all the electric field we have the electric field that comes from the from one and from another cloud so from this cloud and since this is negative this would be like field lines and from positive one.

01:57 This is e1 and e2.

02:00 The total electric field on the plane is equal to the e1 plus e2 addition.

02:09 Now electric field e1 which is the electric field that is acting on the plane due to the first cloud, the lower cloud, can be evaluated from the standard formula.

02:25 This is the electric constant times.

02:28 Q1 which is the charge of the first cloud and the relative difference in the heights.

02:37 And this equals to approximately 9 times 10 to 9 power times 40 over.

02:51 This is due to since we are, this is due to the, we should change this.

03:06 We should change the order so this is h1 minus h2.

03:15 And this is going to be 1 ,000 meters squared, columns squared, but no need for squaring the columns since this is only one...

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