Chapter 16, Problem 38P

To determine

To Find: The direction of electric field at A and B .

Answer to Problem 38P

The electric field is at point A pointing upwards.

The electric field is at point B with an angle above the horizontal.

Explanation of Solution

Given:

Magnitude of charge,

  

  

Horizontal distance from the charge to midpoint E is

  

Vertical distance from the center of the charges to point A is

  

From Pythagorean Theorem the distance between the left side charge to point is

  

From the right-angle triangle

  

Formula used:

Electric field due to charge q at a distance r away from it can be expressed as follows:

  

Here, k is the Coulomb’s constant.

Calculation:

Electric field at point A: since, both the charges are at same distance from point then the horizontal components of electric filed at point A due to both charges will cancel each other. The vertical components of electric field give the net electric field at point .

Electric filed due to both charges can be expressed as

  

On substituting given numerical in the above equation, the electric field at point can be expressed as

  

Electric field at point B:

Point is not symmetrically placed between the charges; hence one must calculate both horizontal and vertical components.

From the triangle BCD the angle made by left side charge at point B is

  

From the triangle BDF, the angle made by right side charge at point B is

  

The distance between left side charges 1 to point B is

  

From the triangle ,the distance between the right-side charge to point B is

  

The net horizontal electric field due to left side charge at point B can be expressed as

  

The net vertical electric field due to right side charge at point B can be expressed as

  

The net electric field at point B can be expressed as

  

The direction of electric field at point B can be expressed as

  

Conclusion:

The electric field is at point B with an angle above the horizontal.