Electric Charges And Fields Chapter-Wise Test 1

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What explains why the electric field inside a charged non-conducting sphere is non-zero and varies with position?

In a non-conductor, charges are fixed and distributed throughout the volume. Gauss’s law shows the field inside depends on the enclosed charge, which increases with radius, leading to a non-zero, position-dependent field.

Charge quantization
Field symmetry
Volume charge distribution
Charge mobility
3

An infinite line charge has \( E = 7.2 \times 10^5 \, \text{N/C} \) at 5 cm. What is \( \lambda \)?

\( E = \frac{2 k \lambda}{r} \).

\( 7.2 \times 10^5 = \frac{2 \times 9 \times 10^9 \times \lambda}{0.05} \).

\( \lambda = \frac{7.2 \times 10^5 \times 0.05}{18 \times 10^9} = 2 \times 10^{-6} \, \text{C/m} \).

\( 1.8 \times 10^{-6} \, \text{C/m} \)
\( 1.9 \times 10^{-6} \, \text{C/m} \)
\( 1.95 \times 10^{-6} \, \text{C/m} \)
\( 2.0 \times 10^{-6} \, \text{C/m} \)
4

What allows an electric dipole to experience a net force in a non-uniform electric field but not in a uniform one?

In a non-uniform field, the field strength varies across the dipole, causing unequal forces on the positive and negative charges. This results in a net force, unlike in a uniform field where equal and opposite forces cancel out.

Charge symmetry
Field gradient
Charge quantization
Field uniformity
2

What ensures that the electric field due to a uniformly charged infinite wire decreases as \( 1/r \) instead of \( 1/r^2 \)?

The cylindrical symmetry of an infinite wire, when analyzed with Gauss’s law, shows the field depends on the radial distance \( r \) with a \( 1/r \) relationship. This arises because the field spreads over a cylindrical surface, not a spherical one like a point charge.

Charge quantization
Field cancellation
Cylindrical symmetry
Charge mobility
3

Which property of electric charge explains why the total charge of an isolated system remains constant even when objects within it are rubbed together?

The conservation of electric charge states that the total charge in an isolated system remains constant over time. When objects are rubbed together, charge is transferred from one to another (e.g., electrons move), but no new charge is created or destroyed. This ensures the net charge of the system stays the same.

Conservation
Quantization
Additivity
Polarity
1

A conducting sphere of radius 21 cm has an electric field of \( 8 \times 10^3 \, \text{N/C} \) at 42 cm from its center. What is the charge?

\( E = \frac{k q}{r^2} \).

\( 8 \times 10^3 = 9 \times 10^9 \times \frac{q}{(0.42)^2} \).

\( q = \frac{8 \times 10^3 \times 0.1764}{9 \times 10^9} = 1.57 \times 10^{-7} \, \text{C} \).

\( 1.4 \times 10^{-7} \, \text{C} \)
\( 1.5 \times 10^{-7} \, \text{C} \)
\( 1.55 \times 10^{-7} \, \text{C} \)
\( 1.57 \times 10^{-7} \, \text{C} \)
4

A thin spherical shell of radius 7 cm has \( q = 3 \, \mu\text{C} \). What is the electric field at 4 cm from the center?

Inside shell (\( r < R \)): \( E = 0 \) (Gauss’s law).

\( 1.5 \times 10^6 \, \text{N/C} \)
\( 1.0 \times 10^6 \, \text{N/C} \)
\( 0 \, \text{N/C} \)
\( 0.5 \times 10^6 \, \text{N/C} \)
3

A charge of \( 17 \, \mu\text{C} \) is at the center of a cube of edge 55 cm. What is the flux through one face?

Total flux: \( \phi = \frac{q}{\varepsilon_0} = \frac{17 \times 10^{-6}}{8.854 \times 10^{-12}} = 1.92 \times 10^6 \, \text{Nm}^2/\text{C} \).

Flux per face (6 faces): \( \phi_{\text{face}} = \frac{1.92 \times 10^6}{6} = 3.2 \times 10^5 \, \text{Nm}^2/\text{C} \).

\( 3.0 \times 10^5 \, \text{Nm}^2/\text{C} \)
\( 3.2 \times 10^5 \, \text{Nm}^2/\text{C} \)
\( 3.3 \times 10^5 \, \text{Nm}^2/\text{C} \)
\( 3.4 \times 10^5 \, \text{Nm}^2/\text{C} \)
2

A plane sheet has \( \sigma = 1.062 \times 10^{-10} \, \text{C/m}^2 \). What is the electric field near it?

\( E = \frac{\sigma}{2 \varepsilon_0} \).

\( E = \frac{1.062 \times 10^{-10}}{2 \times 8.854 \times 10^{-12}} = 6 \, \text{N/C} \).

\( 5.5 \, \text{N/C} \)
\( 6.0 \, \text{N/C} \)
\( 6.5 \, \text{N/C} \)
\( 7.0 \, \text{N/C} \)
2

Why can’t electric field lines form closed loops in electrostatics, unlike magnetic field lines?

Electric field lines begin at positive charges and end at negative charges (or infinity), reflecting the conservative nature of the electrostatic field. Closed loops would imply a non-conservative field, which contradicts Coulomb’s law and Gauss’s law in static conditions.

Charge quantization
Field symmetry
Conservative nature
Superposition effect
3

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