Electric Charges and Fields Chapter-Wise Test 15

Correct answer Carries: 4.

Wrong Answer Carries: -1.

In an experiment, a charged object is brought near a neutral conductor, causing charge separation. What phenomenon is responsible for this effect?

Electrostatic induction occurs when a charged object induces a separation of charges in a neutral conductor. The electric field of the charged object attracts opposite charges and repels like charges, redistributing them without direct contact.

Conduction
Electrostatic induction
Charge quantization
Superposition
2

An infinite line charge has \( \lambda = 7 \times 10^{-7} \, \text{C/m} \). What is the electric field at 25 cm?

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

\( E = \frac{2 \times 9 \times 10^9 \times 7 \times 10^{-7}}{0.25} = 5.04 \times 10^4 \, \text{N/C} \).

\( 4.8 \times 10^4 \, \text{N/C} \)
\( 5.04 \times 10^4 \, \text{N/C} \)
\( 5.2 \times 10^4 \, \text{N/C} \)
\( 5.5 \times 10^4 \, \text{N/C} \)
2

A uniform field \( E = 9 \times 10^3 \, \text{N/C} \) is along the x-axis. What is the flux through a rectangle of 35 cm × 45 cm in the yz-plane?

Area: \( A = 0.35 \times 0.45 = 0.1575 \, \text{m}^2 \).

Flux: \( \phi = E A \cos 0^\circ = 9 \times 10^3 \times 0.1575 = 1417.5 \, \text{Nm}^2/\text{C} \).

1400 \( \text{Nm}^2/\text{C} \)
1410 \( \text{Nm}^2/\text{C} \)
1417.5 \( \text{Nm}^2/\text{C} \)
1420 \( \text{Nm}^2/\text{C} \)
3

A thin spherical shell of radius 10 cm has \( q = 8 \, \mu\text{C} \). What is the electric field at 15 cm from the center?

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

\( E = 9 \times 10^9 \times \frac{8 \times 10^{-6}}{(0.15)^2} = 9 \times 10^9 \times \frac{8 \times 10^{-6}}{0.0225} = 3.2 \times 10^6 \, \text{N/C} \).

\( 3.0 \times 10^6 \, \text{N/C} \)
\( 3.1 \times 10^6 \, \text{N/C} \)
\( 3.15 \times 10^6 \, \text{N/C} \)
\( 3.2 \times 10^6 \, \text{N/C} \)
4

An infinite line charge has \( \lambda = 9 \times 10^{-7} \, \text{C/m} \). What is the electric field at 30 cm?

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

\( E = \frac{2 \times 9 \times 10^9 \times 9 \times 10^{-7}}{0.3} = 5.4 \times 10^4 \, \text{N/C} \).

\( 5.0 \times 10^4 \, \text{N/C} \)
\( 5.4 \times 10^4 \, \text{N/C} \)
\( 5.6 \times 10^4 \, \text{N/C} \)
\( 6.0 \times 10^4 \, \text{N/C} \)
2

Why does the electric field near a charged surface exhibit a sharp increase in strength compared to regions further away?

The inverse-square law governs the field from charges on the surface. Near the surface, the distance \( r \) is small, making \( 1/r^2 \) large, resulting in a strong field that weakens rapidly as distance increases.

Charge quantization
Field symmetry
Charge mobility
Inverse-square law
4

Two point charges \( 6 \times 10^{-7} \, \text{C} \) and \( 10 \times 10^{-7} \, \text{C} \) are 120 cm apart in vacuum. What is the magnitude of the force between them?

Using Coulomb’s law: \( F = k \frac{|q_1 q_2|}{r^2} \).

\( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \), \( q_1 = 6 \times 10^{-7} \, \text{C} \), \( q_2 = 10 \times 10^{-7} \, \text{C} \), \( r = 1.2 \, \text{m} \).

\( |q_1 q_2| = 6 \times 10 \times 10^{-14} = 60 \times 10^{-14} \, \text{C}^2 \).

\( r^2 = (1.2)^2 = 1.44 \, \text{m}^2 \).

\( F = 9 \times 10^9 \times \frac{60 \times 10^{-14}}{1.44} = 9 \times 10^9 \times 4.167 \times 10^{-13} = 0.00375 \, \text{N} \).

0.00375 N
0.0040 N
0.0045 N
0.0050 N
1

A thin spherical shell of radius 28 cm has \( q = 8 \, \mu\text{C} \). What is the electric field at 20 cm from the center?

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

\( 1.8 \times 10^6 \, \text{N/C} \)
\( 1.5 \times 10^6 \, \text{N/C} \)
\( 0 \, \text{N/C} \)
\( 1.0 \times 10^6 \, \text{N/C} \)
3

What property of the electric field allows it to exert a force on a charge without physical contact?

The field’s ability to act at a distance is due to its nature as a force mediator. Generated by charges, it extends through space, influencing other charges via the force \( F = qE \), without requiring direct interaction.

Charge quantization
Action at a distance
Field symmetry
Charge mobility
2

Two point charges \( 7 \times 10^{-7} \, \text{C} \) and \( -2 \times 10^{-7} \, \text{C} \) are 70 cm apart in vacuum. What is the magnitude of the force between them?

Using Coulomb’s law: \( F = k \frac{|q_1 q_2|}{r^2} \).

\( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \), \( q_1 = 7 \times 10^{-7} \, \text{C} \), \( q_2 = -2 \times 10^{-7} \, \text{C} \), \( r = 0.7 \, \text{m} \).

\( |q_1 q_2| = 7 \times 2 \times 10^{-14} = 14 \times 10^{-14} \, \text{C}^2 \).

\( r^2 = (0.7)^2 = 0.49 \, \text{m}^2 \).

\( F = 9 \times 10^9 \times \frac{14 \times 10^{-14}}{0.49} = 9 \times 10^9 \times 2.857 \times 10^{-13} = 0.00257 \, \text{N} \).

0.00257 N
0.0028 N
0.0030 N
0.0032 N
1

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