Suppose a charge q is placed at point x=0, y=0 . A second charge q is placed at point x=8.0 m, y

step 1 Hi, in the given problem there are x -axis and y -axis. This is x -axis horizontal and this is y

Suppose a charge q is placed at point x=0, y=0 . A second...

Key Concepts

Field Cancellation

Field cancellation occurs when the vector sum of the electric fields from multiple charges equals zero at a specific point. This often involves carefully choosing the magnitude and sign of a charge so that its electric field exactly negates the contributions from other charges. Recognizing the conditions for cancellation is important in designing configurations with zero net electric field at a desired location.

Vector Addition of Electric Fields

Since electric fields are vector quantities, they must be added component-wise rather than algebraically. This requires breaking each field into its horizontal and vertical components and summing these separately to determine the overall field at a point. Understanding vector addition is key to solving problems where fields from several charges interact.

Coulomb's Law

Coulomb's Law describes the electrostatic interaction between point charges. It states that the magnitude of the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This foundational law is used to calculate the electric field produced by a point charge by considering how the field strength diminishes with distance.

Electric Field Due to a Point Charge

The electric field from a point charge is a vector field that represents the force per unit charge experienced by a small test charge placed in the field. Its magnitude is given by Coulomb's Law divided by the magnitude of the test charge, and its direction is radially outward for positive charges and inward for negative charges. This concept is essential for understanding how charges distribute their influence in space.

Principle of Superposition

The principle of superposition states that when multiple charges are present, the total electric field at any given point is the vector sum of the electric fields due to each individual charge. This means that fields from different sources add up in both magnitude and direction, which is crucial when determining conditions for field cancellation.

Transcript

00:01 Hi, in the given problem there are x -axis and y -axis.

00:10 This is x -axis horizontal and this is y -axis vertical.

00:16 Now there is a charge particle cube whose position is x -0 meter and y also zero meter.

00:28 Means this is put at the origin a.

00:31 Then another charged particle having same magnitude cube, and that is put at a position having x is equal to 8 .0 meter and y is equal to 0.

00:43 So this is the position at the x -axis.

00:46 So this distance, oa, will be 8 .0 meter.

00:52 Then there is another point b.

00:58 There is another point c whose coordinates are 4 .0 meter comma 3 .0 meter means along x axis its distance is 4 .0 meter and along y axis this is 3 .0 meter then one more point b having coordinates x is equal to 4 .0 meter y is equal to 0.

01:34 So, definitely this is the point p lying at the middle of this line of this line of a like this.

01:43 Now, we have to find a charge, let it be capital q, put, which should be put at point b, which should make the net electric field at point c to be equal to zero.

01:57 So suppose the charge to be put at b.

02:10 In order to make the net electric field at c to be 0 is capital q, which we have to find.

02:32 This is unknown.

02:33 So first of all, we find net electric field at c because of only these two charges, small q each, for which we will have to join these distances, o, c and ac.

02:46 And using the symmetry, we conclude the two distances are same.

02:50 O .c.

02:52 Is equal to ac, which actually equal to hypotenuse.

02:55 So it will be given by pythagoros theorem.

02:58 4 square plus 3 square.

03:00 So this distance will come out to be 16 plus 9 means square root of 25 meter means this is 5 meter...

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