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Electric Charges and Fields Set-3 MCQ Online Practice Test | Class 12 | Quiz Tweek

Electric Charges and Fields Set-3

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

Mastery of electric charges and fields is foundational for both CBSE board examinations and competitive tests (JEE/NEET). This chapter develops quantitative tools — Coulomb's law, superposition, field of continuous distributions and Gauss's law — that recur across electrostatics problems and appear in multi-concept questions requiring spatial reasoning and vector addition.

Beyond routine calculations, questions in examinations probe deeper: interpreting field graphs, recognizing symmetry, and applying Gauss's law in non-intuitive contexts. Practising such problems builds the analytic thinking and estimation skills essential to high-scoring board answers and for tackling tougher competitive problems.

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Q1. Two point charges are placed on the $x$ –axis: $+3.0\ \mu\mathrm{C}$ at $x=0$ and $+12.0\ \mu\mathrm{C}$ at $x=0.40\ \mathrm{m}$ . At what point on the line between them (measured from $x=0$ ) is the net electric field zero?

(A)

$0.100\ \mathrm{m}$

(B)

$0.200\ \mathrm{m}$

(C)

$0.133\ \mathrm{m}$

(D)

$0.267\ \mathrm{m}$

Q2. The measured variation of the magnitude of electric field $E$ with distance $r$ from the centre of an object is: for $0\le r<R,\;E\propto r$ and for $r>R,\;E\propto 1/r^{2}$ . Which of the following charge distributions best explains this $E(r)$ behaviour?

(A)

A uniformly charged solid sphere of radius $R$

(B)

A thin spherical conducting shell with all charge on the surface of radius $R$

(C)

A linear charge distribution along a diameter of length $2R$

(D)

A point charge placed at the centre of radius $R$

Q3. Two identical point charges $+2.0\ \mu\mathrm{C}$ are fixed at coordinates $(+a,0)$ and $(-a,0)$ with $a=0.04\ \mathrm{m}$ . What is the magnitude of the resultant electric field at the point $(0,a)$ ? (Use $k=9.0\times10^{9}\ \mathrm{N\,m^{2}/C^{2}}$ .)

(A)

$1.12\times10^{7}\ \mathrm{N/C}$

(B)

$3.15\times10^{6}\ \mathrm{N/C}$

(C)

$4.47\times10^{6}\ \mathrm{N/C}$

(D)

$7.95\times10^{6}\ \mathrm{N/C}$

Q4. Assertion (A): An isolated hollow conducting spherical shell is electrically neutral. If a point charge $+q$ is now placed at the geometric centre of the cavity, an induced charge $-q$ appears uniformly distributed over the inner surface and $+q$ appears on the outer surface.
Reason (R): The total induced charge on the inner surface equals $-q$ because the conductor was initially neutral and induced charges must sum to cancel the enclosed charge.

(A)

Both A and R are true and R is the 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.

Q5. A thin circular ring of radius $R=0.10\ \mathrm{m}$ carries total charge $Q=5.0\ \mu\mathrm{C}$ uniformly. Find the magnitude of electric field on the axis of the ring at a point which is at a distance $x=R$ from the centre. (Use $k=9.0\times10^{9}\ \mathrm{N\,m^{2}/C^{2}}$ .)

(A)

$4.50\times10^{5}\ \mathrm{N/C}$

(B)

$8.90\times10^{5}\ \mathrm{N/C}$

(C)

$1.59\times10^{6}\ \mathrm{N/C}$

(D)

$2.50\times10^{6}\ \mathrm{N/C}$

Q6. For a uniformly charged thin ring of radius $R$ and total charge $Q$ , the axial electric field magnitude is $E(x)=\dfrac{kQx}{(R^{2}+x^{2})^{3/2}}$ for a point on the axis at distance $x$ from the centre. At which $x$ (measured from the centre) is $E(x)$ maximum?

(A)

$x=0$

(B)

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

(C)

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

(D)

$x=R$

Q7. A uniformly charged solid sphere of radius $R=0.40\ \mathrm{m}$ has unknown total charge $Q$ . From an experimental $E(r)$ graph inside the sphere one reads $E(0.10\ \mathrm{m})=2.0\ \mathrm{N/C}$ . Using $E_{\text{inside}}(r)=\dfrac{1}{4\pi\epsilon_0}\dfrac{Q\,r}{R^{3}}$ , estimate $Q$ (take $1/4\pi\epsilon_0=9.0\times10^{9}\ \mathrm{N\,m^{2}/C^{2}}$ ).

(A)

$1.42\times10^{-11}\ \mathrm{C}$

(B)

$1.42\times10^{-9}\ \mathrm{C}$

(C)

$1.42\times10^{-8}\ \mathrm{C}$

(D)

$1.42\times10^{-10}\ \mathrm{C}$

Q8. Two very large parallel insulating sheets carry uniform surface charge densities $+\sigma$ and $-\sigma$ and face each other. If $\sigma=5.0\times10^{-6}\ \mathrm{C/m^{2}}$ , what is the magnitude of the electric field in the region between the sheets? (Take $\epsilon_0=8.85\times10^{-12}\ \mathrm{C^{2}/(N\,m^{2})}$ .)

(A)

$5.65\times10^{5}\ \mathrm{N/C}$

(B)

$2.82\times10^{5}\ \mathrm{N/C}$

(C)

$1.13\times10^{6}\ \mathrm{N/C}$

(D)

$0\ \mathrm{N/C}$

Q9. Assertion (A): For a uniformly charged solid sphere of radius $R$ the electric field at an interior point a distance $r$ from the centre varies as $E\propto r$ (for $r<R$ ).
Reason (R): This linear variation arises because all the charge on a uniformly charged solid sphere is concentrated on its surface.

(A)

Both A and R are true and R is the 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.

Q10. Two point charges $+Q$ and $-Q$ are fixed at $( -a,0,0)$ and $(+a,0,0)$ respectively. Consider a spherical Gaussian surface of radius $r$ centred at the origin with $r<a$ so that neither charge lies inside the surface. Which statement is correct?

(A)

The electric field is zero at every point on the Gaussian surface.

(B)

The net electric flux through the Gaussian surface is zero even though the electric field on the surface is generally non-zero.

(C)

No electric field lines cross the Gaussian surface because it encloses no charge.

(D)

The electric field on the surface must be uniform in magnitude and direction since net enclosed charge is zero.

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