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 1

Concepts and reason

The concepts required to solve the given problem are electric field due to a point charge and the distance formula that gives the distance between the charges and the origin.

First consider the expression for electric field due to a point charge. Then calculate the components of electric field. Express the answer in the form of ordered pair of its components in three significant figures.

Fundamentals

Electric field due to point charge:

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

The electric field due to a point charge,

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

For that, the distance between the point charge and the given point is to be calculated.

Here, and are the points at which the point charges are placed.

Now calculate the components of electric field due to the charges at the origin ‘O’. Finally, express the answers in three significant figures.

Expression for electric field due to a point charge:

Consider the expression for electric field due to a point charge

Distance between the charge 1 and the origin,

Substitute the values,

Distance between the charge 2 and the origin,

Substitute the values,

Substitute for , for and 16 m for .

Substitute for, for and 9 m for 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.

Ans:

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