Electric Charges and Fields Chapter-Wise Test 9

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A uniform electric field \( E = 8 \times 10^3 \, \text{N/C} \) is along the y-axis. What is the flux through a rectangle of 20 cm × 60 cm in the xz-plane?

Area vector \( \Delta \mathbf{S} = 0.2 \times 0.6 = 0.12 \, \text{m}^2 \) along y-axis.

Flux: \( \phi = \mathbf{E} \cdot \Delta \mathbf{S} = 8 \times 10^3 \times 0.12 = 960 \, \text{Nm}^2/\text{C} \).

\( 960 \, \text{Nm}^2/\text{C} \)
\( 1000 \, \text{Nm}^2/\text{C} \)
\( 1050 \, \text{Nm}^2/\text{C} \)
\( 1100 \, \text{Nm}^2/\text{C} \)
1

A point charge \( 12 \, \mu\text{C} \) is at the origin. What is the electric field magnitude at a point 8 m along the x-axis?

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

\( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \), \( q = 12 \times 10^{-6} \, \text{C} \), \( r = 8 \, \text{m} \).

\( E = 9 \times 10^9 \times \frac{12 \times 10^{-6}}{(8)^2} = 9 \times 10^9 \times \frac{12 \times 10^{-6}}{64} = 1.6875 \times 10^3 \, \text{N/C} \).

\( 1.69 \times 10^3 \, \text{N/C} \)
\( 1.8 \times 10^3 \, \text{N/C} \)
\( 2.0 \times 10^3 \, \text{N/C} \)
\( 2.2 \times 10^3 \, \text{N/C} \)
1

An infinite line charge has \( \lambda = 3 \times 10^{-6} \, \text{C/m} \). What is the electric field at 15 cm?

\( E = \frac{2 k \lambda}{r} \), \( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \).

\( E = \frac{2 \times 9 \times 10^9 \times 3 \times 10^{-6}}{0.15} = 3.6 \times 10^5 \, \text{N/C} \).

\( 3.2 \times 10^5 \, \text{N/C} \)
\( 3.6 \times 10^5 \, \text{N/C} \)
\( 4.0 \times 10^5 \, \text{N/C} \)
\( 4.4 \times 10^5 \, \text{N/C} \)
2

A thin spherical shell of radius 8 cm has \( q = 4 \, \mu\text{C} \). What is the electric field at 6 cm from the center?

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

\( 1.0 \times 10^6 \, \text{N/C} \)
\( 0.8 \times 10^6 \, \text{N/C} \)
\( 0 \, \text{N/C} \)
\( 0.5 \times 10^6 \, \text{N/C} \)
3

A conducting sphere of radius 17 cm has a surface charge density of \( 15 \, \mu\text{C/m}^2 \). What is the total charge?

Surface area: \( A = 4 \pi r^2 = 4 \pi (0.17)^2 = 0.1156 \pi \, \text{m}^2 \).

Charge: \( q = \sigma A = 15 \times 10^{-6} \times 0.1156 \pi = 5.45 \times 10^{-6} \, \text{C} \).

\( 5.0 \times 10^{-6} \, \text{C} \)
\( 5.2 \times 10^{-6} \, \text{C} \)
\( 5.45 \times 10^{-6} \, \text{C} \)
\( 5.6 \times 10^{-6} \, \text{C} \)
3

A thin spherical shell of radius 12 cm has a total charge of \( 9 \, \mu\text{C} \). What is the electric field at 15 cm from the center?

Outside shell (\( r > R \)): \( E = \frac{k q}{r^2} \).

\( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \), \( q = 9 \times 10^{-6} \, \text{C} \), \( r = 0.15 \, \text{m} \).

\( E = 9 \times 10^9 \times \frac{9 \times 10^{-6}}{(0.15)^2} = 9 \times 10^9 \times \frac{9 \times 10^{-6}}{0.0225} = 3.6 \times 10^6 \, \text{N/C} \).

\( 3.6 \times 10^6 \, \text{N/C} \)
\( 4.0 \times 10^6 \, \text{N/C} \)
\( 4.5 \times 10^6 \, \text{N/C} \)
\( 5.0 \times 10^6 \, \text{N/C} \)
1

What property of electric charges allows them to be treated as scalars despite their ability to attract or repel?

The additivity of charges means their total value is the algebraic sum of individual charges, treating them as scalars with magnitude and sign (positive or negative). The directional forces (attraction/repulsion) arise from field interactions, not the charge itself.

Quantization
Conservation
Polarity
Additivity
4

What ensures that the electric field lines from a negative charge always terminate on it rather than extend to infinity?

Negative charges attract positive test charges, so field lines, representing the force direction on a positive charge, point inward toward the negative charge. This attraction defines their termination, unlike positive charges where lines extend outward.

Charge quantization
Field symmetry
Charge density
Attraction
4

A point charge \( -6 \, \mu\text{C} \) is at the origin. What is the electric field magnitude at a point 3 m along the y-axis?

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

\( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \), \( q = 6 \times 10^{-6} \, \text{C} \), \( r = 3 \, \text{m} \).

\( E = 9 \times 10^9 \times \frac{6 \times 10^{-6}}{(3)^2} = 9 \times 10^9 \times \frac{6 \times 10^{-6}}{9} = 6 \times 10^3 \, \text{N/C} \).

\( 6 \times 10^3 \, \text{N/C} \)
\( 6.5 \times 10^3 \, \text{N/C} \)
\( 7 \times 10^3 \, \text{N/C} \)
\( 7.5 \times 10^3 \, \text{N/C} \)
1

Two charges \( +2 \, \mu\text{C} \) and \( +3 \, \mu\text{C} \) are 10 cm apart. What is the electric field at a point 5 cm from \( +2 \, \mu\text{C} \) along the line joining them?

Distance from \( +3 \, \mu\text{C} \) = 5 cm.

\( E_1 = 9 \times 10^9 \times \frac{2 \times 10^{-6}}{(0.05)^2} = 7.2 \times 10^6 \, \text{N/C} \) (away).

\( E_2 = 9 \times 10^9 \times \frac{3 \times 10^{-6}}{(0.05)^2} = 1.08 \times 10^7 \, \text{N/C} \) (towards).

Net \( E = 1.08 \times 10^7 - 7.2 \times 10^6 = 3.6 \times 10^6 \, \text{N/C} \) (towards \( +3 \, \mu\text{C} \)).

\( 3.0 \times 10^6 \, \text{N/C} \)
\( 3.6 \times 10^6 \, \text{N/C} \)
\( 4.0 \times 10^6 \, \text{N/C} \)
\( 4.5 \times 10^6 \, \text{N/C} \)
2

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