Electric Charges and Fields Chapter-Wise Test 10

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A uniform field \( E = 6 \times 10^3 \, \text{N/C} \) is along the y-axis. What is the flux through a rectangle of 40 cm × 25 cm in the xz-plane at 45° to the y-axis?

Area: \( A = 0.4 \times 0.25 = 0.1 \, \text{m}^2 \).

Flux: \( \phi = E A \cos 45^\circ = 6 \times 10^3 \times 0.1 \times \frac{\sqrt{2}}{2} = 424.26 \, \text{Nm}^2/\text{C} \).

400 \( \text{Nm}^2/\text{C} \)
410 \( \text{Nm}^2/\text{C} \)
424 \( \text{Nm}^2/\text{C} \)
450 \( \text{Nm}^2/\text{C} \)
3

Two charges \( +12 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) are 60 cm apart. What is the distance from \( +12 \, \mu\text{C} \) where the electric field is zero?

Let \( x \) be distance from \( +12 \, \mu\text{C} \), then \( 0.6 - x \) from \( -3 \, \mu\text{C} \).

\( \frac{12 \times 10^{-6}}{x^2} = \frac{3 \times 10^{-6}}{(0.6 - x)^2} \), \( 12 (0.6 - x)^2 = 3 x^2 \).

\( 4 (0.36 - 1.2 x + x^2) = x^2 \), \( 1.44 - 4.8 x + 4 x^2 = x^2 \).

\( 3 x^2 - 4.8 x + 1.44 = 0 \), \( x = \frac{4.8 \pm \sqrt{23.04 - 17.28}}{6} = \frac{4.8 \pm 2.4}{6} \).

\( x = 0.4 \, \text{m} \) (between charges).

35 cm
38 cm
39 cm
40 cm
4

A point charge \( 10 \, \mu\text{C} \) is at the origin. What is the electric field magnitude at a point 5 m along the z-axis?

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

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

\( E = 9 \times 10^9 \times \frac{10 \times 10^{-6}}{(5)^2} = 9 \times 10^9 \times \frac{10 \times 10^{-6}}{25} = 3.6 \times 10^3 \, \text{N/C} \).

\( 3.6 \times 10^3 \, \text{N/C} \)
\( 4.0 \times 10^3 \, \text{N/C} \)
\( 4.5 \times 10^3 \, \text{N/C} \)
\( 5.0 \times 10^3 \, \text{N/C} \)
1

An infinite line charge has \( E = 6.3 \times 10^5 \, \text{N/C} \) at 7 cm. What is \( \lambda \)?

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

\( 6.3 \times 10^5 = \frac{2 \times 9 \times 10^9 \times \lambda}{0.07} \).

\( \lambda = \frac{6.3 \times 10^5 \times 0.07}{18 \times 10^9} = 2.45 \times 10^{-6} \, \text{C/m} \).

\( 2.3 \times 10^{-6} \, \text{C/m} \)
\( 2.4 \times 10^{-6} \, \text{C/m} \)
\( 2.42 \times 10^{-6} \, \text{C/m} \)
\( 2.45 \times 10^{-6} \, \text{C/m} \)
4

Two charges \( +10 \, \mu\text{C} \) and \( -2 \, \mu\text{C} \) are 80 cm apart. What is the distance from \( +10 \, \mu\text{C} \) where the electric field is zero?

Let \( x \) be distance from \( +10 \, \mu\text{C} \), then \( 0.8 - x \) from \( -2 \, \mu\text{C} \).

\( \frac{10 \times 10^{-6}}{x^2} = \frac{2 \times 10^{-6}}{(0.8 - x)^2} \), \( 10 (0.8 - x)^2 = 2 x^2 \).

\( 5 (0.64 - 1.6 x + x^2) = x^2 \), \( 3.2 - 8 x + 5 x^2 = x^2 \).

\( 4 x^2 - 8 x + 3.2 = 0 \), \( x = \frac{8 \pm \sqrt{64 - 51.2}}{8} = \frac{8 \pm 3.58}{8} \).

\( x = 0.5525 \, \text{m} \) (between charges).

50 cm
52 cm
54 cm
55.25 cm
4

A point charge \( -9 \, \mu\text{C} \) is at the origin. What is the electric field magnitude at a point 6 m along the x-axis?

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

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

\( E = 9 \times 10^9 \times \frac{9 \times 10^{-6}}{(6)^2} = 9 \times 10^9 \times \frac{9 \times 10^{-6}}{36} = 2.25 \times 10^3 \, \text{N/C} \).

\( 2.25 \times 10^3 \, \text{N/C} \)
\( 2.5 \times 10^3 \, \text{N/C} \)
\( 2.75 \times 10^3 \, \text{N/C} \)
\( 3.0 \times 10^3 \, \text{N/C} \)
1

A conducting sphere of radius 27 cm has an electric field of \( 6 \times 10^3 \, \text{N/C} \) at 54 cm from its center. What is the charge?

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

\( 6 \times 10^3 = 9 \times 10^9 \times \frac{q}{(0.54)^2} \).

\( q = \frac{6 \times 10^3 \times 0.2916}{9 \times 10^9} = 1.944 \times 10^{-7} \, \text{C} \).

\( 1.8 \times 10^{-7} \, \text{C} \)
\( 1.9 \times 10^{-7} \, \text{C} \)
\( 1.92 \times 10^{-7} \, \text{C} \)
\( 1.944 \times 10^{-7} \, \text{C} \)
4

A plastic rod gains \( 4.8 \times 10^{-8} \, \text{C} \) of negative charge when rubbed. How many electrons were transferred to it?

Negative charge means electrons are gained.

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

\( n = \frac{q}{|e|} = \frac{4.8 \times 10^{-8}}{1.6 \times 10^{-19}} = 3 \times 10^{11} \).

\( 3 \times 10^{11} \)
\( 3.5 \times 10^{11} \)
\( 4 \times 10^{11} \)
\( 4.5 \times 10^{11} \)
1

An infinite line charge has \( \lambda = 1.2 \times 10^{-6} \, \text{C/m} \). What is the electric field at 40 cm?

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

\( E = \frac{2 \times 9 \times 10^9 \times 1.2 \times 10^{-6}}{0.4} = 5.4 \times 10^4 \, \text{N/C} \).

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

A glass rod is rubbed with silk and acquires a charge of \( +2.5 \times 10^{-7} \, \text{C} \). How many electrons were transferred from the glass rod to the silk?

Charge on glass rod is positive, so electrons are transferred from glass to silk.

Charge of one electron \( e = -1.6 \times 10^{-19} \, \text{C} \).

Number of electrons: \( n = \frac{q}{|e|} = \frac{2.5 \times 10^{-7}}{1.6 \times 10^{-19}} = 1.5625 \times 10^{12} \).

\( 1.25 \times 10^{12} \)
\( 1.56 \times 10^{12} \)
\( 1.80 \times 10^{12} \)
\( 2.00 \times 10^{12} \)
2

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