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Electric Charges and Fields Set-4

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

Electric Charges and Fields is a core chapter in Class 12 Physics because it introduces electric field, flux, Gauss’s law, and the behavior of charges in symmetric systems. These ideas form the base for many later topics in electrostatics and are frequently tested in both conceptual and numerical form.

For CBSE boards, this chapter is important because it often appears through direct formula-based questions and stepwise reasoning problems. For JEE and NEET, it is even more valuable since symmetry, flux arguments, and field calculations can quickly lead to the correct answer without lengthy computation.

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Q1. A point charge $q$ is placed at one vertex of a cube of side $a$ . The electric flux through the face opposite to that vertex is:

(A)

$\frac{q}{8\varepsilon_0}$

(B)

$\frac{q}{12\varepsilon_0}$

(C)

$\frac{q}{24\varepsilon_0}$

(D)

$\frac{q}{6\varepsilon_0}$

Q2. A non-conducting solid sphere of radius $R$ has volume charge density $\rho(r)=\rho_0\frac{r}{R}$ for $0\le r\le R$ . If $E(r)$ is the electric field magnitude at distance $r$ from the centre, then the ratio $\frac{E(R/2)}{E(R)}$ is:

(A)

$\frac{1}{4}$

(B)

$\frac{1}{2}$

(C)

$\frac{3}{4}$

(D)

$\frac{1}{8}$

Q3. Three point charges $+q$ , $+q$ , and $-q$ are placed at the vertices of an equilateral triangle of side $a$ . The magnitude and direction of the electric field at the centroid are:

(A)

$\frac{3kq}{a^2}$ , towards the $-q$ vertex

(B)

$0$

(C)

$\frac{9kq}{a^2}$ , towards the $-q$ vertex

(D)

$\frac{6kq}{a^2}$ , towards the $-q$ vertex

Q4. For an electric dipole with charges $\pm q$ separated by $2a$ , a point $P$ lies on the extension of the dipole axis beyond the $+q$ charge. If the magnitude of the field due to the nearer charge at $P$ is four times that due to the farther charge, the distance of $P$ from the midpoint is:

(A)

$x=2a$

(B)

$x=3a$

(C)

$x=4a$

(D)

$x=6a$

Q5. A very long non-conducting cylinder of radius $R$ has volume charge density $\rho(r)=\rho_0\left(1-\frac{r^2}{R^2}\right)$ for $0\le r\le R$ . The electric field inside the cylinder is maximum at:

(A)

$r=R\sqrt{\frac{2}{3}}$

(B)

$r=\frac{R}{2}$

(C)

$r=\frac{R}{\sqrt{2}}$

(D)

$r=\frac{2R}{3}$

Q6. An electric dipole consists of charges $+q$ and $-q$ separated by $2a$ . A point $P$ lies on the perpendicular bisector at a distance $a$ from the midpoint. The magnitude of the electric field at $P$ is

(A)

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

(B)

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

(C)

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

(D)

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

Q7. Two point charges $+4q$ and $-q$ are fixed on the $x$ -axis at $x=0$ and $x=d$ , respectively. The net electric field becomes zero at

(A)

a point between the charges, at distance $\dfrac{d}{3}$ from $+4q$

(B)

a point on the $x$ -axis at a distance $d$ from the charge $-q$ , on its outer side

(C)

a point on the $x$ -axis at a distance $d$ from the charge $+4q$ , on its outer side

(D)

midway between the charges

Q8. A solid non-conducting sphere of radius $R$ has volume charge density $\rho(r)=\rho_0\dfrac{r}{R}$ . If $E_1$ is the field at $r=\dfrac{R}{2}$ and $E_2$ at $r=R$ , then $\dfrac{E_1}{E_2}$ equals

(A)

$4$

(B)

$2$

(C)

$\dfrac{1}{4}$

(D)

$\dfrac{1}{2}$

Q9. An isolated point charge $Q$ is placed inside a cube but not at its center. Let $\Phi_{\text{near}}$ be the flux through the face closest to the charge and $\Phi_{\text{far}}$ through the opposite face. For $Q>0$ , which statement must be true?

(A)

$\Phi_{\text{near}}=\Phi_{\text{far}}$

(B)

$\Phi_{\text{near}}<\Phi_{\text{far}}$

(C)

$\Phi_{\text{near}}=\dfrac{Q}{6\varepsilon_0}$

(D)

$\Phi_{\text{near}}>\Phi_{\text{far}}$

Q10. Four point charges are placed at the vertices of a square of side $a$ . Three charges are $+q$ and the fourth corner carries $-q$ . The magnitude of the electric field at the center of the square is

(A)

$\dfrac{4kq}{a^2}$

(B)

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

(C)

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

(D)

$0$

Q11. Two charges $+q$ at $x=0$ and $-4q$ at $x=d$ are fixed on the $x$ -axis. Where is the only point on the axis where the net electric field can be zero?

(A)

Between the charges at $x=\frac{d}{3}$

(B)

On the negative $x$ -axis at a distance $d$ from $+q$

(C)

On the positive $x$ -axis beyond $-4q$ at a distance $d$ from $-4q$

(D)

No such point exists

Q12. A dipole of moment $p$ is placed in a uniform electric field $E$ . The angle between $\vec p$ and $\vec E$ changes from $30^\circ$ to $60^\circ$ , while the field magnitude becomes twice. The torque on the dipole changes by a factor of

(A)

$2\sqrt{3}$

(B)

$\sqrt{3}$

(C)

$2$

(D)

$\frac{1}{2\sqrt{3}}$

Q13. An isolated conducting sphere carries net charge $+Q$ . A spherical cavity is made inside it, and a point charge $+q$ is placed exactly at the centre of the cavity. The charges induced on the inner and outer surfaces are, respectively,

(A)

$-q$ and $Q+q$

(B)

$-Q$ and $q$

(C)

$+q$ and $Q-q$

(D)

$-q$ and $Q-q$

Q14. A point charge $q$ is placed at one vertex of a cube of side $a$ , with the cube occupying the positive octant and the charge at the common vertex. The electric flux through one of the three faces that do not touch the charge is

(A)

$\frac{q}{8\varepsilon_0}$

(B)

$\frac{q}{12\varepsilon_0}$

(C)

$\frac{q}{24\varepsilon_0}$

(D)

$0$

Q15. For an ideal dipole, the magnitude of electric field at a point on the equatorial line at distance $r$ from its centre is $E_0$ . At the same distance $r$ , the field magnitude at a point making $45^\circ$ with the dipole axis is

(A)

$\sqrt{\frac{3}{2}}\,E_0$

(B)

$\sqrt{\frac{5}{2}}\,E_0$

(C)

$2E_0$

(D)

$\frac{1}{\sqrt{2}}\,E_0$

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