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Electric Charges and Fields Set-5 MCQ Online Practice Test | Class 12 | Quiz Tweek

Electric Charges and Fields Set-5

Practice Important MCQs for Electric Charges and Fields — Physics, Class 12.

The chapter “Electric Charges and Fields” is central to CBSE boards and competitive exams because it links electrostatics with core tools like Coulomb’s law, superposition of fields, electric field due to symmetric charge distributions, conductors/shell theorems, and the method of images. These ideas repeatedly appear in higher-level problems involving equilibrium, maximum/minimum field conditions, and quick vector reasoning.

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Q1. Two point charges $+q$ and $-q$ are fixed on the x‑axis at $x=0$ and $x=a$ respectively. What is the net electric field at the midpoint $x=\dfrac{a}{2}$ ?

(A)

$\vec{E}=0$

(B)

$\displaystyle \vec{E}=\frac{8kq}{a^2}\,\hat{i}\quad\text{(to the right)}$

(C)

$\displaystyle \vec{E}=-\frac{4kq}{a^2}\,\hat{i}\quad\text{(to the left)}$

(D)

$\displaystyle \vec{E}=\frac{2kq}{a^2}\,\hat{i}\quad\text{(to the right)}$

Q2. Two point charges $+Q$ and $+4Q$ are located at $x=0$ and $x=d$ on the x‑axis. At which point on the x‑axis (measured from $x=0$ ) is the net electric field zero?

(A)

$x=\dfrac{d}{2}$

(B)

$x=\dfrac{d}{4}$

(C)

$x=\dfrac{2d}{3}$

(D)

$x=\dfrac{d}{3}$

Q3. Two identical point charges $Q$ are placed at $x=\pm a$ on the x‑axis. At a point on the perpendicular bisector (y‑axis) the magnitude of the net electric field depends on $y$ . For what positive value of $y$ is the magnitude of the electric field maximal?

(A)

$y=\dfrac{a}{\sqrt{2}}$

(B)

$y=a$

(C)

$y=\dfrac{a}{\sqrt{3}}$

(D)

$y=\dfrac{a}{2}$

Q4. Statement I: When a point charge $q$ is placed at an off‑centre position inside a hollow neutral conducting spherical shell, the electric field outside the shell is identical to that produced by a point charge $q$ placed at the centre of the shell.
Statement II: This occurs because the outer surface of the spherical conductor is an equipotential, which forces the induced positive charge on the outer surface to distribute uniformly and hence produce a spherically symmetric external field.

(A)

Both statements are true but Statement II does not correctly explain Statement I.

(B)

Statement I is true and Statement II is false.

(C)

Both statements are true and Statement II correctly explains Statement I.

(D)

Statement I is false but Statement II is true.

Q5. A solid insulating sphere of radius $R$ has uniform volume charge density $\rho$ . A spherical cavity of radius $a$ is carved out so that the center of the cavity is at distance $d$ from the centre of the original sphere (assume $d+a\le R$ ). What is the electric field at the centre of the cavity?

(A)

$\displaystyle \vec{E}=\vec{0}$

(B)

$\displaystyle \vec{E}=\frac{\rho\,d}{3\epsilon_0}\,\hat{r}\quad\text{(directed from the original sphere centre toward the cavity centre)}$

(C)

$\displaystyle \vec{E}=\frac{\rho\,d}{\epsilon_0}\,\hat{r}$

(D)

$\displaystyle \vec{E}=\frac{\rho\,a}{3\epsilon_0}\,\hat{r}$

Q6. Two point charges + $q$ and + $4q$ are fixed on the x‑axis at $x=0$ and $x=d$ respectively. At what point between them (measured from the charge at $x=0$ ) is the resultant electric field zero?

(A)

$x=\dfrac{d}{2}$

(B)

$x=\dfrac{d}{4}$

(C)

$x=\dfrac{d}{3}$

(D)

No point exists between them

Q7. An equilateral triangle of side $a$ has charges $+q$ at vertices $A$ and $B$ and a charge $-q$ at vertex $C$ . Let $O$ be the centroid. The magnitude and direction of the electric field at $O$ is

(A)

$E=0$

(B)

$E=\dfrac{6kq}{a^{2}}$ directed towards vertex $C$ (the vertex carrying $-q$ )

(C)

$E=\dfrac{3kq}{a^{2}}$ directed towards $C$

(D)

$E=\dfrac{6kq}{a^{2}}$ directed away from vertex $C$

Q8. A thin uniformly charged ring of radius $R$ carries total charge $Q$ . On the axis of the ring the axial electric field magnitude $E(x)$ (at a distance $x$ from the centre) has a maximum at which value of $x$ ?

(A)

$x=\dfrac{R}{2}$

(B)

$x=R$

(C)

$x=\dfrac{R}{\sqrt{3}}$

(D)

$x=\dfrac{R}{\sqrt{2}}$

Q9. A point charge $q$ is placed at a point $P$ inside a thin, isolated, neutral conducting spherical shell (the charge $q$ is not at the centre). Which one of the following statements is correct?

(A)

The inner surface acquires total induced charge $-q$ (distributed non‑uniformly), the outer surface acquires $+q$ (uniformly), and the electric field outside the shell is identical to that of a point charge $q$ placed at the centre of the spherical shell.

(B)

The inner surface acquires $-q$ but the outer surface carries zero net charge; the field outside is determined by the off‑centre internal charge and is not spherically symmetric.

(C)

No induced charge appears on the inner surface; a charge $+q$ appears on the outer surface and the outside field is as if $q$ were at the actual location $P$ .

(D)

Inner surface has $-q$ and outer has $+q$ , but the outer surface charge distribution depends on $P$ so the outside field is not the same as that of a central point charge.

Q10. A point charge $+q$ is held at a distance $d$ from an infinite grounded conducting plane. Using the image‑charge idea, the magnitude of the attractive force on the charge and the net induced charge on the plane are respectively

(A)

$F=\dfrac{q^{2}}{8\pi\varepsilon_{0}d^{2}}\,,\quad Q_{\rm induced}=-\dfrac{q}{2}$

(B)

$F=\dfrac{q^{2}}{16\pi\varepsilon_{0}d^{2}}\,,\quad Q_{\rm induced}=-q$

(C)

$F=\dfrac{q^{2}}{4\pi\varepsilon_{0}d^{2}}\,,\quad Q_{\rm induced}=-2q$

(D)

$F=\dfrac{q^{2}}{32\pi\varepsilon_{0}d^{2}}\,,\quad Q_{\rm induced}=-\dfrac{q}{4}$

Q11. Two point charges $+Q$ and $-2Q$ are fixed on the x‑axis at $x=0$ and $x=d$ respectively. Locate the point(s) on the x‑axis where the net electric field is zero. Express the coordinate(s) $x$ in terms of $d$ .

(A)

$x=+d(\sqrt{2}-1)$

(B)

$x=-d\sqrt{2}$

(C)

$x=-\dfrac{d}{1+\sqrt{2}}$

(D)

$x=\dfrac{d}{\sqrt{2}-1}$

Q12. A thin ring of radius $R$ carries total charge $Q$ uniformly distributed. The magnitude of the electric field on its axis at a distance $x$ from the centre is $E(x)=\dfrac{1}{4\pi\varepsilon_0}\dfrac{Qx}{(x^2+R^2)^{3/2}}$ . For $x>0$ , at what value of $x$ does $|E(x)|$ attain its maximum?

(A)

$x=R$

(B)

$x=\dfrac{R}{\sqrt{3}}$

(C)

$x=R\sqrt{2}$

(D)

$x=\dfrac{R}{\sqrt{2}}$

Q13. Four point charges are placed at the corners of a square of side $a$ located at coordinates $(\pm a/2,\pm a/2)$ . Three corners carry charge $+q$ and the corner at $(-a/2,-a/2)$ carries charge $-q$ . What is the magnitude and direction of the resultant electric field at the centre of the square?

(A)

$E=\dfrac{4kq}{a^2}$ directed towards the corner carrying $-q$

(B)

$E=\dfrac{2kq}{a^2}$ directed towards the corner carrying $-q$

(C)

$E=\dfrac{4kq}{a^2}$ directed towards the corner opposite to the $-q$ corner

(D)

$E=0$

Q14. A point charge $+q$ is held at a distance $d$ above an infinite grounded conducting plane. Using the method of images, the magnitude of the attractive force between the charge and the plane is

(A)

$F=\dfrac{kq^{2}}{2d^{2}}$

(B)

$F=\dfrac{kq^{2}}{d^{2}}$

(C)

$F=\dfrac{kq^{2}}{4d^{2}}$

(D)

$F=\dfrac{kq^{2}}{8d^{2}}$

Q15. A solid insulating sphere of radius $R$ has uniform volume charge density $\rho$ . A spherical cavity of radius $R/2$ is carved out such that the centre of the cavity is at a distance $R/2$ from the centre of the original sphere. What is the electric field at the centre of the cavity?

(A)

$E=\dfrac{\rho R}{3\varepsilon_0}$

(B)

$E=\dfrac{\rho R}{6\varepsilon_0}$ directed from the sphere's centre toward the cavity centre

(C)

$E=0$

(D)

$E=\dfrac{\rho R}{12\varepsilon_0}$

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