Electric Charges and Fields Chapter-Wise Test 17

Correct answer Carries: 4.

Wrong Answer Carries: -1.

Why does the electric field due to a dipole have both radial and tangential components at a general point?

The dipole’s field results from two opposite charges, creating a complex pattern. At a general point, the field vectors from each charge have different directions, resolving into radial (along the line from the dipole) and tangential (perpendicular) components due to asymmetry.

Charge quantization
Field symmetry
Vector addition
Charge density
3

An infinite line charge has \( E = 3.6 \times 10^5 \, \text{N/C} \) at 10 cm. What is \( \lambda \)?

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

\( 3.6 \times 10^5 = \frac{2 \times 9 \times 10^9 \times \lambda}{0.1} \).

\( \lambda = \frac{3.6 \times 10^5 \times 0.1}{18 \times 10^9} = 2 \times 10^{-6} \, \text{C/m} \).

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

A point charge \( q = 5 \, \mu\text{C} \) is placed at the origin. What is the electric field magnitude at a point 2 m away along the x-axis?

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

\( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \), \( q = 5 \times 10^{-6} \, \text{C} \), \( r = 2 \, \text{m} \).

\( E = 9 \times 10^9 \times \frac{5 \times 10^{-6}}{(2)^2} = 9 \times 10^9 \times \frac{5 \times 10^{-6}}{4} = 1.125 \times 10^4 \, \text{N/C} \).

\( 9.0 \times 10^3 \, \text{N/C} \)
\( 1.125 \times 10^4 \, \text{N/C} \)
\( 1.5 \times 10^4 \, \text{N/C} \)
\( 2.25 \times 10^4 \, \text{N/C} \)
2

A conducting sphere of radius 20 cm has an electric field of \( 3 \times 10^3 \, \text{N/C} \) at 40 cm from its center. What is its charge?

For a conductor, \( E = \frac{k q}{r^2} \) outside.

\( 3 \times 10^3 = 9 \times 10^9 \times \frac{q}{(0.4)^2} \).

\( q = \frac{3 \times 10^3 \times 0.16}{9 \times 10^9} = 5.33 \times 10^{-8} \, \text{C} \).

\( 4.0 \times 10^{-8} \, \text{C} \)
\( 5.33 \times 10^{-8} \, \text{C} \)
\( 6.0 \times 10^{-8} \, \text{C} \)
\( 7.2 \times 10^{-8} \, \text{C} \)
2

A plastic rod gains a charge of \( -1.28 \times 10^{-7} \, \text{C} \) when rubbed. How many electrons were transferred to it?

Negative charge means electrons gained.

\( q = n e \), \( e = -1.6 \times 10^{-19} \, \text{C} \).

\( n = \frac{q}{|e|} = \frac{1.28 \times 10^{-7}}{1.6 \times 10^{-19}} = 8 \times 10^{11} \).

\( 8 \times 10^{11} \)
\( 8.5 \times 10^{11} \)
\( 9 \times 10^{11} \)
\( 9.5 \times 10^{11} \)
1

A thin spherical shell of radius 18 cm has \( q = 12 \, \mu\text{C} \). What is the electric field at 22 cm from the center?

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

\( E = 9 \times 10^9 \times \frac{12 \times 10^{-6}}{(0.22)^2} = 9 \times 10^9 \times \frac{12 \times 10^{-6}}{0.0484} = 2.23 \times 10^6 \, \text{N/C} \).

\( 2.0 \times 10^6 \, \text{N/C} \)
\( 2.1 \times 10^6 \, \text{N/C} \)
\( 2.2 \times 10^6 \, \text{N/C} \)
\( 2.23 \times 10^6 \, \text{N/C} \)
4

A spherical shell has a net flux of \( 1.13 \times 10^5 \, \text{Nm}^2/\text{C} \) through it. What is the charge enclosed?

\( \phi = \frac{q}{\varepsilon_0} \).

\( q = \phi \varepsilon_0 = 1.13 \times 10^5 \times 8.854 \times 10^{-12} = 1.0 \times 10^{-6} \, \text{C} = 1 \, \mu\text{C} \).

\( 0.5 \, \mu\text{C} \)
\( 0.8 \, \mu\text{C} \)
\( 1.0 \, \mu\text{C} \)
\( 1.2 \, \mu\text{C} \)
3

What characteristic of conductors allows charges to distribute uniformly over their surface when placed in an external electric field?

In conductors, charges (free electrons) can move freely. In an external field, they redistribute until the internal field cancels the external field, achieving equilibrium. This results in charges residing only on the surface, distributed uniformly for a spherical conductor due to symmetry.

Mobility of charges
Insulating property
Charge quantization
Fixed charge positions
1

A uniform electric field \( E = 7 \times 10^3 \, \text{N/C} \) is along the x-axis. What is the flux through a rectangle of 25 cm × 40 cm in the yz-plane?

Area vector \( \Delta \mathbf{S} = 0.25 \times 0.4 = 0.1 \, \text{m}^2 \) along x-axis.

Flux: \( \phi = \mathbf{E} \cdot \Delta \mathbf{S} = 7 \times 10^3 \times 0.1 = 700 \, \text{Nm}^2/\text{C} \).

\( 700 \, \text{Nm}^2/\text{C} \)
\( 750 \, \text{Nm}^2/\text{C} \)
\( 800 \, \text{Nm}^2/\text{C} \)
\( 850 \, \text{Nm}^2/\text{C} \)
1

An infinite line charge has \( E = 6.0 \times 10^5 \, \text{N/C} \) at 3 cm. What is \( \lambda \)?

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

\( 6.0 \times 10^5 = \frac{2 \times 9 \times 10^9 \times \lambda}{0.03} \).

\( \lambda = \frac{6.0 \times 10^5 \times 0.03}{18 \times 10^9} = 1 \times 10^{-6} \, \text{C/m} \).

\( 0.8 \times 10^{-6} \, \text{C/m} \)
\( 0.9 \times 10^{-6} \, \text{C/m} \)
\( 0.95 \times 10^{-6} \, \text{C/m} \)
\( 1.0 \times 10^{-6} \, \text{C/m} \)
4

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