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 $(x, y)=$ $(0 \mathrm{cm}, 5.0 \mathrm{cm}),(-5.0 \mathrm{cm},-5.0 \mathrm{cm}),$ and $(-5.0 \mathrm{cm}, 5.0 \mathrm{cm}) 7$ 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 $(x, y)=$ $(0 \mathrm{cm}, 5.0 \mathrm{cm}),(-5.0 \mathrm{cm},-5.0 \mathrm{cm}),$ and $(-5.0 \mathrm{cm}, 5.0 \mathrm{cm}) 7$
Write each electric field vector in component form.
b. Draw a field diagram showing the electric field vectors at these points.

Key Concepts

Coulomb's Law

Coulomb's Law defines the force between two point charges and, by extension, the electric field produced by a single point charge. It establishes that the magnitude of the electric field is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance from the charge, with the direction given by the radial line from the charge. This law is fundamental for calculating the electric field around point charges.

Electric Field Vector

The electric field is a vector quantity that describes the force exerted per unit positive charge at any point in space. It is often expressed in component form, breaking it down into its coordinate system directions (e.g., x and y components). This vector representation is crucial for understanding both the magnitude and direction of the field at various points.

Coordinate System and Unit Vectors

Using a coordinate system and unit vectors allows for the decomposition of an electric field into its components along the defined axes. Unit vectors provide a way to express the field's direction, while the respective scalar components quantify the field's magnitude in each direction. This approach is essential when dealing with problems involving multiple dimensions.

Electric Field Diagrams

Electric field diagrams visually represent the direction and relative magnitude of the electric field at various points in space. These diagrams typically use arrows to indicate the field vectors, where the arrow's direction shows the direction of the field and its length represents its magnitude. Such diagrams provide an intuitive understanding of how the field behaves around charges.

Transcript

00:01 I have drawn the direction of the electric fields at each position because the source charge is negative, all electric field point toward the source charge as i drew.

00:14 And now let's calculate the strength of the electric field for each position, for the position at the 0 .5 centimeter for the first position, we can tell that the distance from this position to the source charge is 5 times 10 to negative 2 meters.

00:40 And we calculate the strength of this electric field by using the formula k times the q divided by r square.

00:52 And we get the number 4 .3 times 10 to 4 newton per cooler.

00:58 And the direction of this electric field is pointing downward, which means it has a negative y component.

01:10 So we can rewrite this electric field in the component form, which is negative 4 .3 times 10 to 4 times the j unit vector newton perkunum.

01:27 And for the second position at negative 5 cm and 5 cm, the distance from this position to the source charge is the r2 equals to 5 times square root of 2 times 10 to negative 2 meters.

01:53 And we can calculate the magnitude of the electric field with the same formula, k times the absolute value of q divided by r2 square.

02:11 And we get the result is 2 .16 times 10 to 4 newton per cooler.

02:20 And then we can calculate the x and y component for the e2 as the x and y component the e2x and e2y have the same length.

02:41 So the e2x equals to e2y and they both equals to e2y...

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