In a rectangular coordinate system a positive point charge q=6.00 ×10^-9 C is placed at the poin

step 1 but air of the given problem. The electric field at region at origin he's, ah zero. This is beca

In a rectangular coordinate system a positive point charge...

In a rectangular coordinate system a positive point charge $q=6.00 \times 10^{-9} \mathrm{C}$ is placed at the point $x=+0.150 \mathrm{~m}, y=0,$ and an identical point charge is placed at $x=-0.150 \mathrm{~m}, y=0 .$ Find the $x$ - and $y$ -components, the magnitude, and the direction of the electric field at the following points: (a) the origin; (b) $x=0.300 \mathrm{~m}, y=0$ (c) $x=0.150 \mathrm{~m}, y=-0.400 \mathrm{~m}$ (d) $x=0, y=0.200 \mathrm{~m}$

In a rectangular coordinate system a positive point charge $q=6.00 \times 10^{-9} \mathrm{C}$ is placed at the point $x=+0.150 \mathrm{~m}, y=0,$ and an identical point charge is placed at $x=-0.150 \mathrm{~m}, y=0 .$ Find the $x$ - and $y$ -components, the magnitude, and the direction of the electric field at the following points:
(a) the origin;
(b) $x=0.300 \mathrm{~m}, y=0$
(c) $x=0.150 \mathrm{~m}, y=-0.400 \mathrm{~m}$
(d) $x=0, y=0.200 \mathrm{~m}$

Key Concepts

Coulomb's Law

Coulomb's Law describes the electric field produced by a point charge, stating that the magnitude of the field is proportional to the charge and inversely proportional to the square of the distance from the charge. This concept is fundamental for calculating the field at a given point in space due to a single charge, using the formula E = k|q|/r², where k is the electrostatic constant.

Superposition Principle

The superposition principle states that the net electric field created by multiple charges is the vector sum of the electric fields produced by each individual charge. This concept allows one to calculate the combined effect of several point charges by adding their respective field contributions in a coordinate system.

Electric Field Vector Components

The electric field, being a vector quantity, has components in different directions. Breaking the field into x- and y-components involves using trigonometric functions based on the geometry of the situation, which facilitates the computation of the resultant field when multiple charges are involved.

Vector Magnitude and Direction

Once the x- and y-components of the electric field are known, the overall magnitude of the field is determined using the Pythagorean theorem, and its direction is found through trigonometric relationships such as the arctan function. This process is essential for fully characterizing the vector field in both its size and orientation.

Transcript

00:01 But air of the given problem.

00:01 The electric field at region at origin he's, ah zero.

00:09 This is because the magnitude off each field is equal, but in in opposite direction.

00:17 Opposite direction, direction but me at the point.

00:24 Ah bee the electric field off the first and second austin second charge are in the same direction and is given by e and to be cake eun bi.

00:40 Bi bi are one square plus cake.

00:43 You divide by on two square.

00:46 This is ah nine times 10 to the power nine times six times 10 to power minus nine one, divided by 0.15 square plus warm derived by 0.45 square.

01:00 This use us electric field to be 2.67 times 10 to the power tree newton for coolum.

01:09 The electric field, due to the first charge is given by them.

01:14 See he won is given by minus.

01:18 Q q one divided by our one square s.

01:22 J from your minus nine times.

01:24 Don't our nine times six times center power minus nine.

01:28 Divided by is it important? four square? this is inge a direction.

01:34 This is minus 337 j.

01:37 Newton got a cool um, for the second charge, the angle between the field line and the horizontal is a better which is written is staying in worse off.

01:47 Why do you ride by two ex? this is ah staying in worse off zero point full divided by 0.3.

01:57 This gives us 53.13 degrees.

02:01 Now the magnitude is he too will be kei kun right by our two square that is a scary times killed right by two x where, um plus y square.

02:14 This is 216 newton for coolum.

02:20 The field component is given by again...

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