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Electric Charges and Fields Set-4 MCQ Online Practice Test | Class 12 | Quiz Tweek

Electric Charges and Fields Set-4

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

Mastery of "Electric Charges and Fields" builds the foundation for understanding electrostatics problems in both board examinations and competitive tests. This chapter introduces Coulomb's law, superposition, electric field and potential due to discrete and continuous charge distributions, and Gauss's law — concepts that recur in complex problems in JEE/NEET as parts of multi-step reasoning and calculus-based derivations.

Beyond routine problems, competitive exams test ability to apply Gauss's law in non-standard geometries, analyze field/potential relations, use image charges, and reason about conductors and shielding. Practising problems that combine algebra, vector decomposition, and qualitative interpretation of graphs is essential to score well and develop physical intuition.

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Q1. Three identical point charges $q$ are placed at three vertices of a square of side $a$ (one vertex is empty). What is the magnitude of the resultant electric field at the centre of the square?

(A)

$\dfrac{2kq}{a^{2}}$

(B)

$\dfrac{kq}{a^{2}}$

(C)

$\dfrac{\sqrt{2}\,kq}{a^{2}}$

(D)

$0$

Q2. A point charge $q$ is placed at the centre of an isolated thin conducting spherical shell of radius $R$ which carries an excess charge $Q$ . For $r>R$ , the magnitude of electric field at distance $r$ from the centre is:

(A)

$\dfrac{1}{4\pi\epsilon_{0}}\dfrac{q+Q}{r^{2}}$

(B)

$\dfrac{1}{4\pi\epsilon_{0}}\dfrac{q}{r^{2}}$

(C)

$\dfrac{1}{4\pi\epsilon_{0}}\dfrac{Q}{r^{2}}$

(D)

$0$

Q3. Three identical charges $+q$ are fixed at the vertices of an equilateral triangle of side $a$ . A fourth charge $+2q$ is brought from infinity and placed at the centroid. The work done by external agent (quasi-statically) in assembling this charge at the centroid is:

(A)

$\dfrac{6\sqrt{3}\,kq^{2}}{a}$

(B)

$\dfrac{3\sqrt{3}\,kq^{2}}{a}$

(C)

$\dfrac{6kq^{2}}{a}$

(D)

$\dfrac{2\sqrt{3}\,kq^{2}}{a}$

Q4. A uniformly charged thin ring of radius $R$ and total charge $Q$ produces on its axis an axial field $E(x)=\dfrac{1}{4\pi\epsilon_{0}}\dfrac{Qx}{(x^{2}+R^{2})^{3/2}}$ . For $x>0$ , the value of $x$ at which $E(x)$ is maximum is:

(A)

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

(B)

$R$

(C)

$\sqrt{2}\,R$

(D)

$\dfrac{R}{2}$

Q5. Assertion (A): The electric field inside the hollow cavity of an isolated conductor is zero when there are no charges in the cavity and only external charges are present. Reason (R): Free charges in the conductor redistribute to the outer surface so as to cancel any field produced by external charges inside the cavity.

(A)

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

(B)

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

(C)

A is true but R is false

(D)

A is false but R is true

Q6. Two equal positive point charges $+Q$ are placed at $x=+a$ and $x=-a$ . At the origin:

(A)

Electric field $\vec{E}=0$ and potential $V=0$

(B)

$\vec{E}=0$ and $V$ is finite positive

(C)

$\vec{E}\neq 0$ and $V=0$

(D)

$\vec{E}\neq 0$ and $V$ is finite positive

Q7. A dipole consists of charges $+q$ at $x=+a$ and $-q$ at $x=-a$ . At a point $P$ on the positive $y$ –axis $(0,y)$ with $y>a$ , which of the following is true?

(A)

Electric potential $V_P=0$ and $\vec{E}_P$ points along $+y$

(B)

$V_P=0$ and $\vec{E}_P$ points along $-x$

(C)

$V_P\neq 0$ and $\vec{E}_P$ points along $-x$

(D)

$V_P=0$ and $\vec{E}_P$ points along $+x$

Q8. A point charge $q$ is held at distance $d$ from a grounded infinite conducting plane. The magnitude of the attractive force exerted by the plane on the charge is:

(A)

$\dfrac{1}{16\pi\epsilon_{0}}\cdot\dfrac{q^{2}}{d^{2}}$

(B)

$\dfrac{1}{4\pi\epsilon_{0}}\cdot\dfrac{q^{2}}{d^{2}}$

(C)

$\dfrac{1}{8\pi\epsilon_{0}}\cdot\dfrac{q^{2}}{d^{2}}$

(D)

$0$

Q9. The radial electric field of a spherically symmetric charge distribution is plotted as $E(r)\propto r$ for $r\le R$ and $E(r)\propto 1/r^{2}$ for $r\ge R$ . Which statement about the volume charge density $\rho(r)$ for $r<R$ is correct?

(A)

$\rho(r)$ is uniform (constant positive)

(B)

$\rho(r)\propto 1/r^{2}$

(C)

$\rho(r)=0$

(D)

$\rho(r)$ is negative constant

Q10. Two point charges $+Q$ and $+4Q$ are fixed at $x=0$ and $x=d$ respectively. At the point $x=\dfrac{d}{3}$ (between them) the net electric field is zero. The electric potential at that point equals:

(A)

$\dfrac{9kQ}{d}$

(B)

$0$

(C)

$-\dfrac{kQ}{d}$

(D)

$\dfrac{3kQ}{d}$

Q11. A point charge $+q$ is placed off-centre inside a neutral hollow conducting spherical shell (no external fields). Which of the following statements are correct?
(i) An induced charge $-q$ appears on the inner surface in a non-uniform distribution.
(ii) The outer surface acquires charge $+q$ distributed uniformly.
(iii) The electric field outside the shell is identical to that of a point charge $+q$ located at the centre.

(A)

Only (i)

(B)

(i) and (ii) only

(C)

(ii) and (iii) only

(D)

(i), (ii) and (iii)

Q12. Assertion (A): For any closed Gaussian surface entirely inside a metallic conductor in electrostatic equilibrium, the net enclosed charge is zero. Reason (R): In electrostatic equilibrium, the electric field inside the bulk of a conductor is zero, so flux through such a surface is zero and hence enclosed charge is zero.

(A)

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

(B)

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

(C)

A is true but R is false

(D)

A is false but R is true

Q13. A point charge $+Q$ is placed at the centre of a neutral thin spherical conducting shell (inner radius $a$ , outer radius $b$ ). After equilibrium, the induced charge on the inner surface and outer surface respectively are:

(A)

$-Q$ on inner, $+Q$ on outer

(B)

$+Q$ on inner, $-Q$ on outer

(C)

$0$ on inner, $0$ on outer

(D)

$-Q/2$ on inner, $+Q/2$ on outer

Q14. Two point charges $+q$ and $-q$ are placed at $x=-a$ and $x=+a$ respectively. The electric field and potential at the origin $(x=0)$ are:

(A)

$\vec{E}=\dfrac{2kq}{a^{2}}\hat{i}$ and $V=0$

(B)

$\vec{E}=0$ and $V=0$

(C)

$\vec{E}=\dfrac{2kq}{a^{2}}\hat{i}$ and $V=\dfrac{2kq}{a}$

(D)

$\vec{E}=0$ and $V=\dfrac{2kq}{a}$

Q15. A thin insulating rod of length $L$ carries uniform charge $+Q$ and lies along the $x$ –axis from $x=0$ to $x=L$ . At a point $P$ on the $x$ –axis at $x=-d$ (with $d>0$ ), the electric field points:

(A)

along $+x$ and its magnitude is $\dfrac{1}{4\pi\epsilon_{0}}\dfrac{Q}{d(d+L)}$

(B)

along $-x$ and its magnitude is $\dfrac{1}{4\pi\epsilon_{0}}\dfrac{Q}{d(d+L)}$

(C)

along $+x$ and its magnitude is $\dfrac{1}{4\pi\epsilon_{0}}\dfrac{Q}{d+L}$

(D)

along $-x$ and its magnitude is $\dfrac{1}{4\pi\epsilon_{0}}\dfrac{Q}{(d+L)^{2}}$

...and 15 more challenging questions available in the interactive simulator.

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