A+12 nC charge is located at the origin. a. What are the...

$A+12$ nC charge is located at the origin. a. What are the electric fields at the positions $(x, y)=$ $(5.0 \mathrm{cm}, 0 \mathrm{cm}),(-5.0 \mathrm{cm}, 5.0 \mathrm{cm}),$ and $(-5.0 \mathrm{cm},-5.0 \mathrm{cm}) ?$ Write each electric field vector in component form. b. Draw a field diagram showing the electric field vectors at these points.

$A+12$ nC charge is located at the origin.
a. What are the electric fields at the positions $(x, y)=$ $(5.0 \mathrm{cm}, 0 \mathrm{cm}),(-5.0 \mathrm{cm}, 5.0 \mathrm{cm}),$ and $(-5.0 \mathrm{cm},-5.0 \mathrm{cm}) ?$
Write each electric field vector in component form.
b. Draw a field diagram showing the electric field vectors at these points.

Key Concepts

Field Diagram

A field diagram is a graphical representation of the electric field at various points in space. It uses arrows to indicate the direction and relative magnitude of the electric field vectors, helping to visualize how the field emanates from or converges toward a charge.

Coordinate System

A coordinate system allows the spatial positions of points and vectors to be clearly specified. In electric field problems, a Cartesian coordinate system (using x and y coordinates) is typically employed to define points in space and to compute the corresponding field components.

Vector Representation

Since the electric field is a vector quantity, it is commonly represented in component form. This means breaking down the field into its horizontal and vertical (or x and y) components relative to a chosen coordinate system, which facilitates precise mathematical and graphical analysis.

Coulomb's Law

Coulomb's law provides the mathematical framework to calculate the magnitude and direction of the electric field produced by a point charge. It states that the electric field magnitude is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance from the charge, with the field directed radially outward for positive charges and inward for negative charges.

Electric Field

An electric field is a vector field that represents the force per unit charge at any point in space. It describes how a test charge would be influenced by an electric force if placed in the field. The electric field not only has a magnitude (indicating the force strength) but also a direction (indicating the force’s orientation).

Point Charge

A point charge is an idealized model for a charged particle where the charge is considered to be concentrated at a single point in space. This simplification allows the use of Coulomb’s law without having to account for the charge’s physical dimensions.

Transcript

00:01 I have drawn the directions of the electric fields at each position.

00:07 So our next step is to calculate the strengths of the electric field at each position and write the electric field in component form.

00:18 So let's first look at the electric field at the first position at the 5 cm, zero position.

00:28 And we can tell that the r here, the distance from this position to the source charge is 5 cm, which is 5 times 10 to negative 2 meters.

00:44 And we can calculate the strength of this electric field by using the formula 1 equals to 10 k times q divided by r square.

00:57 And we plug in all the numbers and get the result 4 .3 times 10 to 4 newtons per column.

01:07 And we can write this electric field in a component form, considering the direction of this electric field, which is 4 .3 times 1024 times the unit vector, newton per column.

01:30 And for the second position, negative 5 cm and 5 cm, the distance from this position to the source charge is 5 times square root of 2 times 10 to negative 2 meters.

01:54 And again, we calculate the strength of the electric field at this position by using the same formula.

02:04 And we can easily get the result is 2 .16 times 10 to 4 newton per cooler.

02:15 And to write this electric field in component form, we need to calculate the x component.

02:25 The e2x, e2x, as well as the y component, e2y, for this electric field...

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