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Question

Find the electric field at the origin, point O.

Give the x and y components of the electric field as an ordered pair. Express your answer in newtons per coulomb to three significant figures. Keep in mind that an x component that points to the right is positive and a y component that points upward is positive.

Answer “Find the electric field at the origin, point O. Give the x and y components of the electric field as an ordered pair”.

Concepts and reason

To solve the problem, you will need to understand the electric field due to a single charge and the distance formula which gives the distance between charges and their origin.

Consider the electric field due to point charges first. Next, calculate the x- and y-components of an electric field. Then, express the answer as an ordered pair of its components in three significant numbers.

Fundamentals

Electric field due to point charge:

The “force acting per unit of charge” is called the electric field. The electric field direction is the direction of force exerts on a unit positive charge.

A point charge creates an electric field,

Here, E is the electric field, ɛ₀ is the permittivity of the free space, q is the point charge and r is the distance between the charges.

Calculate the x and y components of the electric field caused by the charges at the source ‘O. Finally, you can express your answers using three significant figures.

Expression for an electric field due to the point charge:

Take the expression “electric field due to a single charge” in mind.

Distance between the charge 1 and the origin,

Substitute the values,

Distance between the charge 2 and the origin,

Substitute the values,

Substitute 9 x 10⁹ N m²/C² for k, 8nC for q₁ and 16m for r₁

x – component of electric field due to the charge 1 at the point O,

Substitute 9 x 10⁹ N m²/C² for k, 6nC for q₂ and 9m for r₂ to find the x component of electric field due to the charge 2 at the point O is,

Net electric field along the x – direction,

Here the point charges are lying on the x axis. Hence the y – component of electric field is zero.

E_y = 0N/C

Answer:

x and y components of electric field is, 0.385 N/C, 0N/C

Last words

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