Electric field and electric field lines — practice questions

Question 1 · difficulty L2 · understanding

A stream of a positively charged particles having $${q \over m} = 2 \times {10^{11}}{C \over {kg}}$$ and velocity $${\overrightarrow v _0} = 3 \times {10^7}\widehat i\,m/s$$ is deflected by an electric field $$1.8\widehat j$$ kV/m. The electric field exists in a region of 10 cm along $$x$$ direction. Due to the electric field, the deflection of the charge particles in the $$y$$ direction is _________ mm.

Question 2 · difficulty L2 · understanding

A long cylindrical volume contains a uniformly distributed charge of density $$\rho \,\mathrm{Cm}^{-3}$$. The electric field inside the cylindrical volume at a distance $$x=\frac{2 \varepsilon_{0}}{\rho} \mathrm{m}$$ from its axis is ________ $$\mathrm{Vm}^{-1}$$.

Question 3 · difficulty L2 · understanding

A thin half ring of radius 35 cm is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at centre of the half ring is $100 \mathrm{~V} / \mathrm{m}$, then the value of $Q$ is $\_\_\_\_$ nC . $$\left(\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2 \text { and } \pi=3.14\right)$$

• A. 2.14
• B. 2.44
• C. 3.25
• D. 0.7

Question 4 · difficulty L2 · understanding

A point charge $+q$ is placed at the origin. A second point charge $+9 q$ is placed at ($\mathrm{d}, 0,0$) in Cartesian coordinate system. The point in between them where the electric field vanishes is:

• A. $(3 \mathrm{d} / 4,0,0)$
• B. $(\mathrm{d} / 4,0,0)$
• C. $(4 \mathrm{d} / 3,0,0)$
• D. $(\mathrm{d} / 3,0,0)$

Question 5 · difficulty L2 · understanding

Two charges $$q$$ and $$3 q$$ are separated by a distance '$$r$$' in air. At a distance $$x$$ from charge $$q$$, the resultant electric field is zero. The value of $$x$$ is :

• A. $$\frac{r}{3(1+\sqrt{3})}$$
• B. $$\frac{(1+\sqrt{3})}{r}$$
• C. $$\frac{r}{(1+\sqrt{3})}$$
• D. $$r(1+\sqrt{3})$$

Question 6 · difficulty L2 · understanding

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero. Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces. In the light of the above statements, choose the most appropriate answer from the options given below :

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

Question 7 · difficulty L2 · understanding

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

• A. move in the straight line paths in the same direction
• B. move with the uniform velocity throughout from lower potential to higher potential
• C. drift from higher potential to lower potential.
• D. move in the curved paths from lower potential to higher potential

Question 8 · difficulty L2 · understanding

As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $\mathrm{Q}$ in three different regions $\mathrm{I}, \mathrm{II}$ and $\mathrm{III}$ is given by: $(\mathrm{I}: r < a, \mathrm{II}: a < r < b$, III: $r>b$ )

• A. $E_I=0, E_{I I}=0, E_{I I I} \neq 0$
• B. $E_I \neq 0, E_{I I}=0, E_{III}=0$
• C. $E_I \neq 0, E_{I I}=0, E_{III} \neq 0$
• D. $E_I=0, E_{I I}=0, E_{I I I}=0$

Question 9 · difficulty L2 · understanding

Electric field in a certain region is given by $$\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^{2}} \hat{i}+\frac{\mathrm{B}}{y^{3}} \hat{j}\right) \text {. The } \mathrm{SI} \text { unit of } \mathrm{A} \text { and } \mathrm{B}$$ are :

• A. $$\mathrm{Nm}^{2} \mathrm{C} ; \mathrm{Nm}^{3} \mathrm{C}$$
• B. $$\mathrm{Nm}^{3} \mathrm{C}^{-1} ; \mathrm{Nm}^{2} \mathrm{C}^{-1}$$
• C. $$\mathrm{Nm}^{3} \mathrm{C} ; \mathrm{Nm}^{2} \mathrm{C}$$
• D. $$\mathrm{Nm}^{2} \mathrm{C}^{-1} ; \mathrm{Nm}^{3} \mathrm{C}^{-1}$$

Question 10 · difficulty L2 · understanding

A point charge $$2\times10^{-2}~\mathrm{C}$$ is moved from P to S in a uniform electric field of $$30~\mathrm{NC^{-1}}$$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be

• A. 600 mJ
• B. $$-1200$$ mJ
• C. 1200 mJ
• D. $$-600$$ mJ