What is the strength of the electric field at the position indicated by the dot in the figure?
E = _____ N/C
What is the direction of the electric field at the position indicated by the dot in the figure? Specify the direction as an angle above the horizontal line.
θ = ____ ⁰
PLEASE SHOW ALL WORK
The concept used to solve this problem is the electric field due a charged body.
Use the concept of coulomb’s constant, the charge on body, and the distance from the charged body to find the electric field due to x-component of force due to one charged particle.
Use the electric field due to x-component of force due to 1 charged particle to find the strength of the electric field by both the charges at the position indicated by dot.
Use the x-component of the net electric field to find the direction as an angle above the horizontal line.
Write the expression for the electric field due to a charged body.
Here, the Coulomb’s constant is , the charge on body is , and the distance from the charged body is .
The figure below shows the distance between the charges and the dot.
The diagonal line joining the charges and the dot is .
The arrangement of charges with the dot is symmetric and is at equal distance with each other.
Both the charges are positive in nature and hence, they repel each other with the same magnitude. Therefore, y-component of the force is canceled. Hence, only the x-component of force will act on the dot.
Write the expression for the electric field due to x component of force due to one charged particle.
Substitute for , for and for .
Write the expression for the x-component of the electric field due to charge.
Here, the x-component of electric field is .
Substitute for .
The above value of electric field is due to the only on the dot.
Write the expression for the electric field due to both the charges.
Substitute for .
From the above step,
There is only x-component of the net electric field at the dot and hence, the direction of the electric field would be in x-direction and the angle above the horizontal line would be .
Ans:The strength of the electric field at the position indicated by dot is .
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