Question

Question: A hollow ball of radius , made of very thin glass, is rubbed all over with a silk cloth and acquires a negative charge of that is uniformly distributed all over its surface. Location A in Figure 15.64 is inside the sphere, from the surface. Location B in Figure 15.64 is outside the sphere, from the surface. There are no other charged objects nearby.

Which of the following statements about , the magnitude of the electric field due to the ball, are correct? Select all that apply. (a) At location A, is . (b) All of the charges on the surface of the sphere contribute to at location A. (c) A hydrogen atom at location A would polarize because it is close to the negative charges on the surface of the sphere. What is at location B?

Short answer

Answer

(a) The statement (a) is incorrect.

(b) The statement (b) is correct.

(c) at location B is $-1\times {10}^5\text{N/C}$.

Step-by-step solution

Identification of the given data

The given data is listed below as:

• The radius of the hollow ball is,$r=7\text{cm}\times \left(\frac{\text{1}\text{m}}{\text{100}\text{cm}}\right)=0.07\text{m}$
• The charge of the hollow ball is,$Q=-9\times {10}^{-8}\text{C}$
• The distance of the location A from the surface of the sphere is,$l=1\text{cm}\times \left(\frac{\text{1}\text{m}}{\text{100}\text{cm}}\right)=\text{0.01}\text{m}$
• The distance of the location B from the surface of the sphere is,$s=2\text{cm}\times \left(\frac{\text{1}\text{m}}{\text{100}\text{cm}}\right)=\text{0.02}\text{m}$

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 of that object and inversely proportional to the distance between the center of the electric field and the charge.

(a) and (b) Determination of the correct statement

The first statement (a) states that at location A, is . This statement is incorrect as in the center of an insulator, the electric field is zero and the location A is not at the center even though the charge on the sphere’s outside is distributed uniformly.

The second statement (b) states that All of the charges on the surface of the sphere contribute to at location A. This statement is correct as this is the main reason the electrical field of is not zero.

Thus, the statement (a) is incorrect.

The statement (b) is correct.

(c) Determination of  at the location B

The equation of the magnitude of the electric field of the hollow ball at the location B is expressed as:

$E_{\text{ball}}=k\frac{Q}{{\left(r+s\right)}^2}$

Here, is the electric field constant, is the charge of the hollow ball, is the radius of the hollow ball and is the distance of the location B from the surface of the sphere.

Substitute the values in the above equation.

$$\begin{gathered} E_{\text{ball}}=\left(9\times {10}^9\text{N}·{\text{m}}^{\text{2}}{\text{/C}}^{\text{2}}\right)\frac{-9\times {10}^{-8}\text{C}}{{\left(0.07\text{m}+0.02\text{m}\right)}^2} \\ =\frac{-810\text{N}·{\text{m}}^{\text{2}}\text{/C}}{{\left(0.09\text{m}\right)}^2} \\ =\frac{-810\text{N}·{\text{m}}^{\text{2}}\text{/C}}{\left(8.1\times {10}^{-3}{\text{m}}^2\right)} \\ =-1\times {10}^5\text{N/C} \end{gathered}$$

Thus, at location B is$-1\times {10}^5\text{N/C}$ .