A +2.00-nC point charge is at the origin, and a second...

A $+$2.00-nC point charge is at the origin, and a second $-$5.00-nC point charge is on the $x$-axis at $x = $0.800 m. (a) Find the electric field (magnitude and direction) at each of the following points on the x-axis: (i) $x =$ 0.200 m; (ii) $x =$ 1.20 m; (iii) $x = -$0.200 m. (b) Find the net electric force that the two charges would exert on an electron placed at each point in part (a).

Key Concepts

Electric Force on a Charge

The electric force experienced by a charge in an electric field is obtained by multiplying the magnitude of the charge by the electric field at that point. This relationship, expressed as F = qE, is crucial for understanding how charges interact with electric fields and for calculating the forces exerted on them.

Coulomb's Law

Coulomb's Law quantifies the electric force between two point charges. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental in calculating both the magnitude and the direction of forces in electrostatic problems.

Electric Field Due to a Point Charge

The electric field due to a point charge is a measure of the force per unit charge that a test charge would experience at a given point in space. The field is radially directed away from a positive charge and toward a negative charge, and its magnitude is determined by Coulomb’s law by dividing the force by the test charge.

Principle of Superposition

The principle of superposition states that when multiple charges are present, the total electric field at any point is the vector sum of the electric fields created by each individual charge. This concept is essential in solving problems where more than one charge contributes to the net field.

Transcript

00:01 First of all, we need to draw the diagram of the given charges as always remember to draw one.

00:11 It makes our mind clear and our answer more accurate.

00:18 So for that, we need to find the direction and the magnitude of the dielectric field of each charge at point xi is equal to 0 .200 meter.

00:29 And then finding the net electric field at this point.

00:34 So we need to put this point on the x -axis.

00:40 Now, we also know that the electric field of a positive charge is outward from the charge and the electric field of the negative charge is towards the charge.

00:53 Hence, the direction of the electric field exerted on the point x -i is drawn in the figure.

01:03 We know that electric field is given by e is equal to kq upon r square, where r is the distance between the points where the field is calculated and the charge.

01:30 Now, since the two electric fields are directed to the right, as we have seen, so we need to find the sum of the magnitude of both electric fields at point 1, noting that the nate will be directed to the right as well.

01:50 Hence, we can write the formula for the net electric field at point i is equal to k mode q1 upon r1 square plus k q2 upon r2 square in the eye direction.

02:36 Plug the given and note that the distance between the points and the charge are represented here as is equal to 9 .0 into 10 to power 9 into 10 to power 9 into more plus 2 .0 into 10 to power minus 9 upon 0 .200 square plus 9 .0 into 10 to power 9 into more minus 5 .0 into 10 to power minus 9 whole square.

04:14 So this will give us the answer of e -nat will be equivalent to 575 newton per column in i direction.

04:30 Noting that ey -net is equal to 0 newton percolum, let me write e -net in the y -direction is equal to 0 -neuton per -culum.

04:52 Let me write, newton percula since point i is a dimensionless point.

05:01 Now by the same approach as we did above, we will find the distance between the two charges and the new point two.

05:14 We find distances in the figure below and we also draw the directions of the electric field exerted by each charge point.

05:31 So let me draw the diagram.

05:36 This is the line where here we are having charge q1 and here we are having charge q2 and this is the distance x2 and the distance between this two is the distance between this 2 is 0 .4 meter and the distance between this 2 is 1 .20 meter...

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