On the x -axis, in which of the three regions x 3 d is there a point where 𝐄=0

step 1 Hi, in the given problem there is an x -axis shown like this. This is the origin. Suppose point

On the x -axis, in which of the three regions x<0, 0<x<3 d,...

Key Concepts

Region Analysis on the Axis

Determining where along a defined axis the net electric field is zero involves analyzing how the fields from the charges vary over different spatial regions. This typically requires considering the distance from each charge and the sign (direction) of the individual field contributions in those regions, which informs the existence or absence of cancellation points.

Electric Field Cancellation

A point where the electric field is zero is achieved when the vector contributions from all charges exactly cancel each other out. This concept involves analyzing the magnitudes and directions of the individual fields to determine regions where the net field may vanish.

Electric Field

The electric field is a vector field that represents the force experienced by a unit positive test charge placed in the vicinity of other charges. It is defined as the force per unit charge and is central to understanding how charges interact in space.

Superposition Principle

The superposition principle states that when multiple electric fields are present, the net electric field at any point is the vector sum of the individual fields. This principle is crucial for analyzing problems where fields from different sources must be combined to determine the overall effect.

Transcript

00:01 Hi, in the given problem there is an x -axis shown like this.

00:13 This is the origin.

00:16 Suppose point a is representing the origin at which we put a charge q.

00:24 As this is the origin, so x is 0 here.

00:28 Then there is another point, suppose if this is b at which we put a charge 2q.

00:35 Now the total gap between these two points is divided into three parts, each having a gap, each having a length of d.

00:49 So the total gap between these two points is 3d, means the position of this point b can be given as 3d.

01:00 Now in this problem we have to discuss the position of zero electric field at the x -axis whether it is in the region where x is less than zero or it is in the region where x is more than 3d or it is in a region where x is lying between 0 and 3d.

01:27 So, to discuss this position of the zero electric field, first of all, if we consider this position of zero electric field here in the region x less than zero and the point is supposed it to be p.

01:44 Then we know the electric field always goes away from the positive charge.

01:49 So the two electric fields here, ea, means due to the charge put at a point a, and electric field due to the charge put at point b, e b, both are in the same direction so they never can be added to give the resultant electric field to be equal to 0.

02:11 So zero electric field is never possible in this region where x is less than zero.

02:16 Now if you consider this observation point to be present here in a region x more than 3d, suppose this is point b.

02:26 Now again using the same rule as electric field goes away from a positive charge...

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