Question

Is the following statement true or false? If true, what principle makes it true? If false, give a counterexample or say why. See Figure 14.67.

“The electric field $E_{point}$at the center of an induced dipole, due to the point charge, is equal in magnitude and opposite in direction to the electric field $E_{\text{dipole}}$at the location of the point charge, due to the induced dipole.”

Short answer

The following statement is trueand the concept of the electric field makes it true.

Step-by-step solution

Significance of the magnitude of the electric field

The electric field is beneficial for an electrically charged particle to exert force on another particle. The electric field is directly proportional to the charge and inversely proportional to the cube of their distances.

Determination of the correctness of the statement

The diagram has been provided below:

From the above diagram, it has been identified that the net electric field’s concept is fulfilled as one of the electric fields has been generated in a particular direction and the other in a different direction.Hence, the direction of the $E_{po\mathrm{int}}$and$E_{\text{dipole}}$are opposite.

The equation of the electric field at the center of an induced dipole due to the point charge is expressed as follows:

$\begin{array}{c}{E}_{po\mathrm{int}}=k\frac{q}{r^3}\\ =-E_{\text{dipole}}\end{array}$

Here, is the electric field constant, $q$is the point charge and$r$ is the distance between the $E_{po\mathrm{int}}$, and $E_{\text{dipole}}$. Hence, the statement is true and the concept of the electric field makes it true.

Thus, the following statement is trueand the concept of the electric field makes it true.