Electric flux and Gauss's law with its applications — practice questions

Question 1 · difficulty L2 · understanding

The electric field in a region is given by $\overrightarrow{\mathrm{E}}=(2 \hat{i}+4 \hat{j}+6 \hat{k}) \times 10^3 \mathrm{~N} / \mathrm{C}$. The flux of the field through a rectangular surface parallel to $x-z$ plane is $6.0 \,\mathrm{Nm}^2 \mathrm{C}^{-1}$. The area of the surface is _____________ $\mathrm{cm}^2$.

Question 2 · difficulty L2 · understanding

An electric field $$\vec{E}=(2 x \hat{i}) N C^{-1}$$ exists in space. A cube of side $$2 \mathrm{~m}$$ is placed in the space as per figure given below. The electric flux through the cube is ______ $$\mathrm{Nm}^2 / \mathrm{C}$$.

Question 3 · difficulty L2 · understanding

An electric field, $$\overrightarrow{\mathrm{E}}=\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}}$$ passes through the surface of $$4 \mathrm{~m}^2$$ area having unit vector $$\hat{n}=\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$$. The electric flux for that surface is _________ $$\mathrm{Vm}$$.

Question 4 · difficulty L2 · understanding

The electric field in a region is given by $$\overrightarrow E = {2 \over 5}{E_0}\widehat i + {3 \over 5}{E_0}\widehat j$$ with $${E_0} = 4.0 \times {10^3}{N \over C}$$. The flux of this field through a rectangular surface area 0.4 m 2 parallel to the Y-Z plane is __________ Nm 2 C $$-$$1 .

Question 5 · difficulty L2 · understanding

The electric field in a region is given by $$\overrightarrow E = \left( {{3 \over 5}{E_0}\widehat i + {4 \over 5}{E_0}\widehat j} \right){N \over C}$$. The ratio of flux of reported field through the rectangular surface of area 0.2 m 2 (parallel to y $$-$$ z plane) to that of the surface of area 0.3 m 2 (parallel to x $$-$$ z plane) is a : b, where a = __________ [Here $${\widehat i}$$, $${\widehat j}$$ and $${\widehat k}$$ are unit vectors along x, y and z-axes respectively.]

Question 6 · difficulty L2 · understanding

Two point charges $8\ \mu C$ and $-2\ \mu C$ are located at $x = 2$ cm and $x = 4$ cm, respectively on the $x$-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is ________.

• A. 4 : 1
• B. 3 : 4
• C. 4 : 3
• D. 4 : 5

Question 7 · difficulty L2 · understanding

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The outer body of an aircraft is made of metal which protects persons sitting inside from lightning strikes. Reason (R) : The electric field inside the cavity enclosed by a conductor is zero. In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• B. (A) is correct but (R) is not correct
• C. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• D. (A) is not correct but (R) is correct

Question 8 · difficulty L2 · understanding

A point charge causes an electric flux of $-2 \times 10^4 \mathrm{Nm}^2 \mathrm{C}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

• A. $17.7 \times 10^{-8} \mathrm{C}$
• B. $-17.7 \times 10^{-8} \mathrm{C}$
• C. $15.7 \times 10^{-8} \mathrm{C}$
• D. $-15.7 \times 10^{-8} \mathrm{C}$

Question 9 · difficulty L2 · understanding

Match List - I with List - II. List - I List - II (A) Electric field inside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. (I) σ/ε 0 (B) Electric field at distance r>0 from a uniformly charged infinite plane sheet with surface charge density σ. (II) σ/2ε 0 (C) Electric field outside (distance r>0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. (III) 0 (D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density σ. (IV) $\frac{\sigma}{\epsilon_0 r^2}$ Choose the correct answer from the options given below :

• A. (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
• B. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
• C. (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
• D. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)

Question 10 · difficulty L2 · understanding

Five charges $$+q,+5 q,-2 q,+3 q$$ and $$-4 q$$ are situated as shown in the figure. The electric flux due to this configuration through the surface $$S$$ is :

• A. $$\frac{q}{\epsilon_0}$$
• B. $$\frac{3 q}{\epsilon_0}$$
• C. $$\frac{5 q}{\epsilon_0}$$
• D. $$\frac{4 q}{\epsilon_0}$$