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Electric Charges and Fields Set-6

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

“Electric Charges and Fields” is a core chapter for both CBSE and competitive exams because it builds the fundamental idea of electric field and potential, enabling students to solve a wide range of problems—from equilibrium and stability to field superposition, Gauss’s law-based results, and dipole/ring/continuous charge distributions.

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Q1. Two point charges $+q$ and $+4q$ are fixed on the $x$ ‑axis at $x=0$ and $x=d$ respectively. At which point on the $x$ ‑axis is the net electric field zero?

(A)

At $x=\dfrac{d}{2}$ measured from the $+q$ towards the $+4q$

(B)

At $x=\dfrac{d}{4}$ measured from the $+q$ towards the $+4q$

(C)

At $x=\dfrac{d}{3}$ measured from the $+q$ towards the $+4q$

(D)

At $x=\dfrac{2d}{3}$ measured from the $+q$ towards the $+4q$

Q2. Charges $+q$ , $+q$ and $-2q$ are placed at the vertices $A,B,C$ of an equilateral triangle of side $a$ . What is the magnitude and direction of the electric field at the centroid?

(A)

$\displaystyle E=\dfrac{9}{4\pi\varepsilon_0}\dfrac{q}{a^2}$ directed from the centroid towards vertex $C$ (the $-2q$ charge)

(B)

$E=0$ at the centroid

(C)

$\displaystyle E=\dfrac{3}{4\pi\varepsilon_0}\dfrac{q}{a^2}$ directed towards $C$

(D)

$\displaystyle E=\dfrac{9}{4\pi\varepsilon_0}\dfrac{q}{a^2}$ directed away from $C$

Q3. A thin insulating wire in the shape of a semicircular arc of radius $R$ carries a uniform linear charge density $\lambda$ . What is the electric field at the centre of the semicircle (magnitude and direction)?

(A)

$\displaystyle E=\dfrac{\lambda}{4\pi\varepsilon_0 R}$ directed downward (towards the chord)

(B)

$\displaystyle E=\dfrac{\lambda}{\pi\varepsilon_0 R}$ directed downward

(C)

$\displaystyle E=\dfrac{\lambda}{2\pi\varepsilon_0 R}$ directed upward (away from the chord)

(D)

$\displaystyle E=\dfrac{\lambda}{2\pi\varepsilon_0 R}$ directed downward (towards the chord)

Q4. A small positive test charge is placed at the midpoint between two equal positive charges fixed at $x=\pm a$ .
Assertion (A): The test charge will be in equilibrium at the midpoint.
Reason (R): The equilibrium is stable because the electric potential has a local minimum at the midpoint.

(A)

Both A and R are true and R is the correct explanation of A

(B)

A is true but R is false

(C)

A is false but R is true

(D)

Both A and R are true but R is not the correct explanation of A

Q5. An isolated neutral conducting spherical shell has a point charge $q$ placed anywhere inside its hollow cavity (not necessarily at the centre).
Assertion (A): The electric field at points outside the shell is identical to that produced by a point charge $q$ located at the centre of the shell.
Reason (R): The outer spherical surface of the conductor acquires induced charge $+q$ which distributes uniformly over the outer surface; this uniform shell produces the same external field as a central point charge.

(A)

Both A and R are true and R is the correct explanation of A

(B)

A is true but R is false

(C)

A is false but R is true

(D)

Both A and R are true but R is not the correct explanation of A

Q6. Two point charges $+Q$ and $+9Q$ are fixed on the $x$ ‑axis at $x=0$ and $x=10\ \text{cm}$ respectively. At what position along the line joining them is the net electric field zero? (Give distance from the charge $+Q$ at $x=0$ .)

(A)

$7.5\ \text{cm}$

(B)

$5.0\ \text{cm}$

(C)

$2.5\ \text{cm}$

(D)

$1.0\ \text{cm}$

Q7. Two identical point charges $+q$ are placed at $(\pm a,0)$ . On the perpendicular bisector (the $y$ ‑axis), at what distance $y$ from the origin is the magnitude of the electric field maximum?

(A)

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

(B)

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

(C)

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

(D)

$y=a$

Q8. Two fixed point charges $+Q$ are at $x=\pm a$ . A particle of mass $m$ and charge $-q$ ( $q>0$ ) is placed at the origin and is constrained to move only along the $y$ ‑axis (perpendicular bisector). For small displacements the motion is simple harmonic. The angular frequency $\omega$ of small oscillations is

(A)

$\displaystyle \omega=\sqrt{\frac{1}{4\pi\epsilon_0}\cdot\frac{Qq}{ma^3}}$

(B)

$\displaystyle \omega=\sqrt{\frac{1}{4\pi\epsilon_0}\cdot\frac{4Qq}{ma^3}}$

(C)

$\displaystyle \omega=\sqrt{\frac{1}{4\pi\epsilon_0}\cdot\frac{2Qq}{ma^2}}$

(D)

$\displaystyle \omega=\sqrt{\frac{1}{4\pi\epsilon_0}\cdot\frac{2Qq}{ma^3}}$

Q9. A point charge $Q$ is fixed at the origin. A small electric dipole made of charges $+q$ and $-q$ separated by $2a$ has its centre at $x=d$ on the $+x$ ‑axis ( $d\gg a$ ) and is oriented so that $-q$ is nearer the origin. Using the dipole moment $p=2aq$ , the net force on the dipole to leading order in $a/d$ is:

(A)

$\displaystyle \mathbf{F}=+\frac{2}{4\pi\epsilon_0}\,\frac{Qp}{d^3}\,\hat{\mathbf{x}}$

(B)

$\displaystyle \mathbf{F}=-\frac{2}{4\pi\epsilon_0}\,\frac{Qp}{d^3}\,\hat{\mathbf{x}}$

(C)

$\displaystyle \mathbf{F}=-\frac{1}{4\pi\epsilon_0}\,\frac{Qp}{d^3}\,\hat{\mathbf{x}}$

(D)

$\displaystyle \mathbf{F}=-\frac{2}{4\pi\epsilon_0}\,\frac{Qp}{d^2}\,\hat{\mathbf{x}}$

Q10. A thin circular ring of radius $R$ carries total charge $Q$ uniformly. Along the ring axis the electric field magnitude is $E(x)=\dfrac{1}{4\pi\varepsilon_0}\dfrac{Qx}{(x^2+R^2)^{3/2}}$ . (i) At what axial distance $x$ is $E(x)$ maximum? (ii) What is the maximum value $E_{\rm max}$ ? Choose the correct pair.

(A)

$x=\dfrac{R}{\sqrt{2}}\quad,\quad E_{\max}=\dfrac{1}{4\pi\varepsilon_0}\,\dfrac{2Q}{3\sqrt{3}\,R^2}$

(B)

$x=\dfrac{R}{2}\quad,\quad E_{\max}=\dfrac{1}{4\pi\varepsilon_0}\,\dfrac{Q}{2R^2}$

(C)

$x=\dfrac{R}{\sqrt{3}}\quad,\quad E_{\max}=\dfrac{1}{4\pi\varepsilon_0}\,\dfrac{3Q}{4R^2}$

(D)

$x=R\quad,\quad E_{\max}=\dfrac{1}{4\pi\varepsilon_0}\,\dfrac{Q}{R^2}$

Q11. Two point charges +2q and +q are fixed on the x‑axis at x = 0 and x = d respectively. A point on the x‑axis between them (0 < x < d) where the net electric field is zero is located at

(A)

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

(B)

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

(C)

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

(D)

No point exists between the charges where the net electric field is zero

Q12. A uniformly charged thin rod of length $L$ with total charge $+Q$ lies along the x‑axis from $x=0$ to $x=L$ . The magnitude of electric field at point $P$ located at $x=-a$ ( $a>0$ ) on the x‑axis is

(A)

$\displaystyle E=\frac{1}{4\pi\varepsilon_0}\frac{Q}{a^2}$

(B)

$\displaystyle E=\frac{1}{4\pi\varepsilon_0}\frac{Q}{a(a+L)}$

(C)

$\displaystyle E=\frac{1}{4\pi\varepsilon_0}\frac{2Q}{a(a+L)}$

(D)

$\displaystyle E=\frac{1}{4\pi\varepsilon_0}\frac{Q}{(a+L)^2}$

Q13. Charges $+q$ and $-q$ are located at $(a,0)$ and $(-a,0)$ respectively. At a point $P$ on the y‑axis at $(0,y)$ ( $y>0$ ), which of the following correctly gives the electric potential $V$ and electric field $\mathbf{E}$ at $P$ ?

(A)

$V=0,\qquad \mathbf{E}=0$

(B)

$V=0,\qquad \mathbf{E}=+\dfrac{1}{4\pi\varepsilon_0}\dfrac{2qa}{(a^2+y^2)^{3/2}}\,\hat{i}$

(C)

$V=0,\qquad \mathbf{E}=-\dfrac{1}{4\pi\varepsilon_0}\dfrac{2qy}{(a^2+y^2)^{3/2}}\,\hat{j}$

(D)

$V=0,\qquad \mathbf{E}=-\dfrac{1}{4\pi\varepsilon_0}\dfrac{2qa}{(a^2+y^2)^{3/2}}\,\hat{i}$

Q14. A point charge $q$ is located at a distance $d$ above an infinite, perfectly conducting grounded plane. The magnitude of the electrostatic force of attraction between the charge and the induced charges on the plane is

(A)

$\displaystyle F=\frac{1}{4\pi\varepsilon_0}\frac{q^2}{4d^2}$

(B)

$\displaystyle F=\frac{1}{4\pi\varepsilon_0}\frac{q^2}{16d^2}$

(C)

$\displaystyle F=\frac{1}{4\pi\varepsilon_0}\frac{q^2}{2d^2}$

(D)

$\displaystyle F=\frac{1}{4\pi\varepsilon_0}\frac{q^2}{8d^2}$

Q15. A thin insulating ring of radius $R$ carries a uniform positive charge $+Q$ on its circumference. A small test charge $q$ is placed on the axis of the ring near its centre. Regarding the equilibrium of the test charge at the centre ( $x=0$ along the axis), which statement is correct?

(A)

Equilibrium at $x=0$ is unstable when $qQ<0$ and stable when $qQ>0$

(B)

Equilibrium at $x=0$ is always stable for any sign of $q$

(C)

Equilibrium at $x=0$ is stable when $qQ<0$ (opposite signs) and unstable when $qQ>0$ (same sign)

(D)

There is no equilibrium at $x=0$ for any finite $q$

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