Question

A positively charged sphere is placed near a neutral block of nickel, as shown in Figure 14.92. (a) Which of the diagrams in Figure 14.93 best represents the equilibrium distribution of charge on the neutral nickel block?

(b) At location P inside the nickel block the electric field due to the charged sphere is $<-625,0,0>\mathbf{}\mathit{N}\mathbf{/}\mathit{C}$. At equilibrium, which of the following statements must be true? (1) It is not possible to determine the electric field at location P due only to charges on the surface of the nickel block. (2) The electric field at location P due only to charges on the surface of the nickel block is $\mathbf{<}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{>}\mathbf{}\mathit{N}\mathbf{/}\mathit{C}$. (3) Because the net electric field at location P is $\mathbf{<}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{>}\mathbf{}\mathit{N}\mathbf{/}\mathit{C}$, the field at P due only to charges on the surface of the polarized nickel block must be $\mathbf{<}\mathbf{625}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{>}\mathbf{}\mathit{N}\mathbf{/}\mathit{C}$.

Short answer

Answer

(a) Diagram B best represents the equilibrium distribution of charge on the neutral nickel block.

(b) Statement 3 is correct.

Step-by-step solution

Identification of given data

The given data can be listed below as:

The electric field due to the charged sphere at the location P is $<-625,0,0>\mathbf{}\mathit{N}\mathbf{/}\mathit{C}$.

Significance of the electric field

The electric field is described as a region that helps an electrically charged particle to exert force on another particle. The magnitude of the electric field is directly proportional to the charge and inversely proportional to the distance of the charges.

(a) Determination of the diagrams that best represents the equilibrium distribution of charge on the neutral nickel block

Here, in the above diagram, as the charged sphere is placed at the left side of the neutral nickel block, then the neutral nickel block will induce positive charges and due to the positive charges, the nickel block will also induce negative charges. Hence, as the block was neutral, then the positive charges will be at the right side and the negative charges will be at the left side of the block.

Thus, diagram B best represents the equilibrium distribution of charge on the neutral nickel block.

(b) Determination of the correct statement

Statement 1 states that it is not possible to determine the electric field at location P due only to charges on the surface of the nickel block. This statement is incorrect as the electric field at location P can be identified with the help of the electric field due to the charged sphere with the help of the equation of the magnitude of the electric field.

Statement 2 states that the electric field at the location P due only to charges on the surface of the nickel block is $<0,0,0>\mathbf{}\mathit{N}\mathbf{/}\mathit{C}$. This statement is incorrect, as the electric field is not zero due to the charges, but as the sphere is in equilibrium, that is the reason the electric field is zero.

The statement 3 states that because the net electric field at location P is $\mathbf{<}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{>}\mathbf{}\mathit{N}\mathbf{/}\mathit{C}$, the field at P due only to charges on the surface of the polarized nickel block must be $\mathbf{<}\mathbf{625}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{>}\mathbf{}\mathit{N}\mathbf{/}\mathit{C}$. This statement is correct as due to equilibrium; the net electric field is zero and the electric field at location P is $\mathbf{<}\mathbf{625}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{>}\mathbf{}\mathit{N}\mathbf{/}\mathit{C}$.

Thus, statement 3 is correct.