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1

One of the following measurement units is equivalent to the electric field measurement unit

\[Kg.m.A^{-1}.s^{-2}\;\;\;\;\;\;-C\]	\[Kg.m.A^{-1}.s^{-3}\;\;\;\;\;\;-A\]
\[Kg.m.A^{-1}.s^{-1}\;\;\;\;\;\;-D\]	\[Kg.m.A^{-2}.s^{-2}\;\;\;\;\;\;-B\]

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2

An electric field with intensity \[E=500\frac{N}{C}\] has an electron placed inside it. The electric force acting on the electron equals: \[q_e=1.6×10^{-19}C\]

\[Fe=4×10^{-17} \;\;N\;\;\;\;\;\;-C\] Opposite to the field direction	\[Fe=4×10^{-17} \;\;N\;\;\;\;\;\;-A\] In the field direction
\[Fe=8×10^{-17} \;\;N\;\;\;\;\;\;-D\] Opposite to the field direction	\[Fe=8×10^{-17} \;\;N\;\;\;\;\;\;-B\] In the field direction

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3

In the figure below, two charges are on the same line \[q_1=+9\;\;nc\;\;\;\;\;\;\;\;q_2=?\] At point \[A\] the electric field is canceled. The magnitude and type of charge \[q_2\] equals

\[q_2= - 3.2 ×10^{-7}\;\;c\;\;\;\;\;\;-C\]	\[q_2= + 1.44 ×10^{-7}\;\;c\;\;\;\;\;\;-A\]
\[q_2= -4.5 ×10^{-7}\;\;c;\;\;\;\;\;-D\]	\[q_2= + 2.25 ×10^{-7}\;\;c\;\;\;\;\;\;-B\]

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4

In the figure below, the field at point \[A\] was calculated \[E_{net}=500\frac{N}{C}\]
and its direction is shown in the drawing. If the magnitude of the electric field produced by the first charge equals \[E_{1}=300\frac{N}{C}\]then the type and magnitude of the second charge equals

\[q_2= - 3.24 ×10^{-9}\;\;c\;\;\;\;\;\;-C\]	\[q_2= - 2.43 ×10^{-9}\;\;c\;\;\;\;\;\;-A\]
\[q_2= + 1.78 ×10^{-9}\;\;c;\;\;\;\;\;-D\]	\[q_2= + 5.67 ×10^{-9}\;\;c\;\;\;\;\;\;-B\]

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5

In the figure below, the field lines for three charges are drawn. One of the following answers is correct

\[q_1(-)\;\;\;\;q_2(+)\;\;\;\;q_3(+) \;\;\;\;\;q_3>q_1>q_2\;\;\;\;\;\;-C\]	\[q_1(+)\;\;\;\;q_2(-)\;\;\;\;q_3(-)\;\;\;\;\;q_1=q_2=q_3\;\;\;\;\;\;-A\]
\[q_1(+)\;\;\;\;q_2(-)\;\;\;\;q_3(-) \;\;\;\;\;q_1>q_2=q_3\;\;\;\;\;\;-D\]	\[q_1(+)\;\;\;\;q_2(-)\;\;\;\;q_3(-)\;\;\;\;\;q_2>q_1>q_3\;\;\;\;\;\;-B\]

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6

(1 ×10^-10m ) A dipole with distance between its poles
( 0.4 m ) The field produced by the dipole was calculated at a point distant from the center of the dipole and along the dipole axis
The field intensity was \[E= 9×10^{-18}\frac{N}{C}\]then the dipole charge equals

\[q= 3.2 ×10^{-19}\;\;c\;\;\;\;\;\;-C\]	\[q= 2.6 ×10^{-19}\;\;c\;\;\;\;\;\;-A\]
\[q= 1.3 ×10^{-19}\;\;c;\;\;\;\;\;-D\]	\[q= 6.4 ×10^{-19}\;\;c\;\;\;\;\;\;-B\]

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7

A positively charged particle is placed inside the field shown in the figure below. One of the following answers represents the motion of the particle:

The particle moves with - C increasing acceleration	The particle moves with - A constant velocity
The particle moves with - D decreasing acceleration	The particle moves with - B constant acceleration

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8

A ball with mass (5g) is dropped to the ground while charged with a charge of (5 µc). The uniform electric field vector that makes it balanced is:

\[E= 1×10^3 \;\;N/C\;\;\;\;\downarrow\;\;\;\;\;\;-C\] Downward	\[E= 9.8×10^3 \;\;N/C\;\;\;\;\downarrow\;\;\;\;\;\;-A\] Downward
\[E= 1×10^3 \;\;N/C\;\;\;\;\uparrow\;\;\;\;\;\;-D\] Upward	\[E= 9.8×10^3 \;\;N/C\;\;\;\;\uparrow\;\;\;\;\;\;-B\] Upward

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9

An electron is projected into a uniform electric field with intensity (E= 1 × 10³N/C)
directed towards the positive vertical axis as shown in the figure below
with a speed of (𝜗=5 × 10⁶m/s) horizontally
and travels a horizontal distance of (8 cm).
In the same time period, it will have a vertical displacement of:

\[ ∆𝑌= 0.011 \;\;m\;\;\;\;\;\;-C\]	\[ ∆𝑌= 0.033 \;\;m\;\;\;\;\;\;-A\]
\[ ∆𝑌= 0.044 \;\;m\;\;\;\;\;\;-D\]	\[ ∆𝑌= 0.022\;\;m\;\;\;\;\;\;-B\]

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10

One of the following shapes has zero torque for an electric dipole in a uniform electric field

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11

( τ= 1.5 × 10^-9N.m ) An electric dipole has maximum torque when
(positive z-axis) and is directed along the
(positive y-axis) in a uniform electric field directed along the
( E = 1 × 10^-3N/C ) with magnitude

\[P=1.5×10^{-6} \;\;c.m\;\;\;\;\;\;-C\] along the positive horizontal axis	\[ P=1.5×10^{-8} \;\;c.m\;\;\;\;\;\;-A\] along the positive horizontal axis
\[P=1.5×10^{-8} \;\;c.m\;\;\;\;\;\;-D\] along the negative horizontal axis	\[P=1.5×10^{-6} \;\;c.m\;\;\;\;\;\;-B\] along the negative horizontal axis

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12

(0.3 m) An infinite wire has an electric field calculated at a point
( 2.5 × 10³N/C ) The electric field magnitude was
and direction is shown in the figure. The number of electrons gained or lost per unit length equals

\[n=2.6×10^{11}\;\;\;\;\;\;-C\] Gained electrons	\[ n=2.6×10^{11} \;\;\;\;\;\;-A\] Lost electrons
\[n=3.4×10^{11}\;\;\;\;\;\;-D\] Gained electrons	\[n=3.4×10^{11}\;\;\;\;\;\;-B\] Lost electrons

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13

One of the following units is a unit of electric flux

\[Kg.m .A^{-1}.S^{-3}\;\;\;\;\;\;-C\]	\[Kg.m^2 .A^{-1}.S^{-3}\;\;\;\;\;\;-A\]
\[Kg.m^3 .A^{-1}.S^{-3}\;\;\;\;\;\;-D\]	\[Kg.m^2 .A^{-1}.S^{-2}\;\;\;\;\;\;-B\]

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14

A spherical shell is charged with a charge of \[-4\;\;µc\] and a charge is placed inside it \[+4\;\;µc\]>then the internal charge \[q_1=?\] and external charge of the spherical shell \[q_2=?\] respectively

\[q_1=+4\;µc \;\;\;\;\;q_2=+4\;µc\;\;\;\;\;\;-C\]	\[q_1=0.0 \;\;\;\;\;q_2=0.0\;\;\;\;\;\;-A\]
\[q_1=-4\;µc \;\;\;\;\;q_2=0.0\;\;\;\;\;\;-D\]	\[q_1=-4\;µc \;\;\;\;\;q_2=+4\;µc\;\;\;\;\;\;-B\]

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15

( A ) Two infinite wires in length with charge densities and dimensions shown in the figure below. The point has a field intensity equal to

\[ E= 4200 \;\;N/C\;\;\;\;\;\longrightarrow\;\;\;\;\;\;-C\] To the right	\[ E= 2800 \;\;N/C\;\;\;\;\;\longleftarrow \;\;\;\;\;\;-A\] To the left
\[E= 4800 \;\;N/C\;\;\;\;\;\longrightarrow\;\;\;\;\;\;-D\] To the right	\[E= 3500 \;\;N/C\;\;\;\;\;\longleftarrow\;\;\;\;\;\;-B\] To the left

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16

Two infinite parallel conducting plates charged with equal charge density. One of the following answers is correct:

\[ EA=EB=EC=ED \;\;\;\;\;\;-C\]	\[EA=EC=0 \;\;\;\;\;, \;\;\;\;\;EB=ED≠0\;\;\;\;\;\;-A\]
\[ EA=EB \;\;\;\;\;, \;\;\;\;\;ED=EC\;\;\;\;\;\;-D\]	\[EA>EC \;\;\;\;\;, \;\;\;\;\;EB=ED \;\;\;\;\;\;-B\]

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17

Two infinite unconnected plates with the same charge. The electric field at point A was calculated to be \[E= 1×10^3\frac{N}{C}\]. The charge density on each plate is:

\[𝛿= 3.6 ×10^{-9} \;\;c/m^2\;\;\;\;\;\;-C\]	\[𝛿= 3.9×10^{-8} \;\;c/m^2\;\;\;\;\;\;-A\]
\[𝛿= 4.8×10^{-9} \;\;c/m^2\;\;\;\;\;\;-D\]	\[𝛿= 8.85×10^{-9} \;\;c/m^2\;\;\;\;\;\;-B\]

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17

Two infinite unconnected plates with the same charge. The electric field at point A was calculated to be \[E= 1×10^3\frac{N}{C}\]. The charge density on each plate is:

\[𝛿= 3.6 ×10^{-9} \;\;c/m^2\;\;\;\;\;\;-C\]	\[𝛿= 3.9×10^{-8} \;\;c/m^2\;\;\;\;\;\;-A\]
\[𝛿= 4.8×10^{-9} \;\;c/m^2\;\;\;\;\;\;-D\]	\[𝛿= 8.85×10^{-9} \;\;c/m^2\;\;\;\;\;\;-B\]

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18

An infinite conducting plate with a charge density of \[6 × 10^{-6} \;\;C/m^2\] was left. A positively charged sphere with a charge of \[+4\;\;nc\] and a mass of \[9 \;\;g\] falls towards the plate. The sphere moves with an acceleration of

\[ a=6.37 \;\;m/s^2\;\;\;\;\;\uparrow \;\;\;\;\;\;-C\] Upwards	\[ a=3.92 \;\;m/s^2\;\;\;\;\;\uparrow \;\;\;\;\;\;-A\] Upwards
\[a=4.52 \;\;m/s^2\;\;\;\;\;\downarrow \;\;\;\;\;\;-D\] Downwards	\[a=9.48 \;\;m/s^2\;\;\;\;\;\downarrow \;\;\;\;\;\;-B\] Downwards

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19

An uncharged spherical shell with an inner radius \[0.5\;] and an outer radius \[0.7\; m\] A point charge was placed inside it as shown in the figure below with a magnitude of \[-6\;µc \] at its center. The electric field intensity at a point located at a distance of \[0.6\; m \]

\[ E=0.0\;\;\;\;\;\;-C\]	\[ E = 2.3 ×10^5 \;\;N/C \;\;\;\;\;\;-A\]
\[ E = 1.5 ×10^5 \;\;N/C\;\;\;\;\;\;-D\]	\[ E = 4.6 ×10^5 \;\;N/C\;\;\;\;\;\;-B\]

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20

The relationship between the electric field and the distance from the surface of a hollow conducting sphere was plotted, resulting in the following graph. The conductor is charged with a charge of

\[q= 1.34×10^{-19} \;\;c\;\;\;\;\;\;-C\]	\[ q= 2.56×10^{-19} \;\;c\;\;\;\;\;\;-A\]
\[q= 2.14×10^{-19} \;\;c\;\;\;\;\;\;-D\]	\[q= 1.78×10^{-19} \;\;c\;\;\;\;\;\;-B\]

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21

The relationship between the electric field and the distance from the center of a charged sphere
with a non-conducting solid was plotted, resulting in the following graph. The magnitude of the electric field at a point located at a distance \[0.15\;m\] from the center of the sphere is equivalent to

\[E=2800 \;\;N/C\;\;\;\;\;\;-C\]	\[E=3000 \;\;N/C\;\;\;\;\;\;-A\]
\[E=2700 \;\;N/C\;\;\;\;\;\;-D\]	\[E=2900 \;\;N/C\;\;\;\;\;\;-B\]

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22

The relationship between the electric field and distance from the center
of a uniformly charged solid non-conducting sphere was plotted,
resulting in the following graph.
The amount of charge contained within a radius of \[0.1\;m\] of the sphere is equivalent to:

\[q= 2.2×10^{-9} \;\;c\;\;\;\;\;\;-C\]	\[ q= 2.45×10^{-9} \;\;c\;\;\;\;\;\;-A\]
\[q= 7.45×10^{-9} \;\;c\;\;\;\;\;\;-D\]	\[q= 1.78×10^{-9} \;\;c\;\;\;\;\;\;-B\]

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23

A solid non-conducting sphere is uniformly charged with radius \[R=0.5\;\; m\]. The field at a point \[r=0.3\;\; m\] from the center of the sphere was calculated to be \[E=4×10^3\frac{N}{C}\]. The charge of the sphere is equivalent to:

\[q= 3.54×10^{-6} \;\;c\;\;\;\;\;\;-C\]	\[ q= 5.71×10^{-6} \;\;c\;\;\;\;\;\;-A\]
\[q= 1.85×10^{-6} \;\;c\;\;\;\;\;\;-D\]	\[q= 6.28×10^{-6} \;\;c\;\;\;\;\;\;-B\]

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24

A spherical shell has a charge of \[-7 \;\;µc \], inner radius \[2 \;\;m\] and outer radius \[4\;\;M\]. The electric field at a point was calculated to be \[E= 3 ×10^3\;\;N/C\] and directed towards the shell. The charge inside the spherical shell is equivalent to:

\[q= +1.67 ×10^{-6} \;\;c\;\;\;\;\;\;-C\]	\[ q= +5.33 ×10^{-6} \;\;c\;\;\;\;\;\;-A\]
\[q= -1.67×10^{-6} \;\;c\;\;\;\;\;\;-D\]	\[q= -5.33×10^{-6} \;\;c\;\;\;\;\;\;-B\]

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25

An electric charge generates an electric field around it. The electric field at point \[A\] was calculated to be \[ E= 6×10^4\;\;N/C \]. The electric field at point \[B\] was calculated to be \[ E= 3×10^4\;\;N/C \]. The ratio between the distances \[\frac{r_A}{r_B}\] is equal to:

\[\frac{r_A}{r_B}=0.5\;\;\;\;\;\;-C\]	\[\frac{r_A}{r_B}=0.4\;\;\;\;\;\;-A\]
\[\frac{r_A}{r_B}=0.25\;\;\;\;\;\;-D\]	\[\frac{r_A}{r_B}=0.7\;\;\;\;\;\;-B\]

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26

In the figure below, a point charge generates an electric field around it. The ratio between the field at point \[A\] to the field at point \[B\] is equal to:

\[\frac{E_A}{E_B}=9\;\;\;\;\;\;-C\]	\[\frac{E_A}{E_B}=4\;\;\;\;\;\;-A\]
\[\frac{E_A}{E_B}=16\;\;\;\;\;\;-D\]	\[\frac{E_A}{E_B}=3\;\;\;\;\;\;-B\]

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27

The figure shows four Gaussian surfaces surrounding charge distributions. Which Gaussian surface has no electric flux through it?

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28

A Gaussian surface shaped like a bean is placed in four different regions of an electric field. This is illustrated by the field lines below.

In which case is the total electric flux through the closed surface the highest?

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29

A positive point charge (+4q)
and a negative point charge (-3q) are placed inside a conducting sphere and a negative point charge is placed outside the sphere with magnitude
One of the following answers correctly represents the results of Gauss's law

Both charges affect with the same -C force but in opposite directions	The charge inside the conductor -A affects with a greater force on the charge outside the conductor
The charge inside the conductor will -D not be affected by a force and the charge outside the conductor is affected by a force	The charge outside the conductor -B affects with a greater force on the charge inside the conductor

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30

(∅=3 ×10²N.m²/c ) A charge was placed inside a spherical surface and the flux on the surface was calculated to be
If the radius of the spherical surface is doubled, the flux on the new surface becomes

\[∅= 6 ×10^2 \;\;N.m^2/C\;\;\;\;\;\;-C\]	\[ ∅= 12 ×10^2 \;\;N.m^2/C\;\;\;\;\;\;-A\]
\[∅= 3 ×10^2 \;\;N.m^2/C\;\;\;\;\;\;-D\]	\[∅= 1.5×10^2 \;\;N.m^2/C\;\;\;\;\;\;-B\]

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31

An electric field with intensity given by the relation \[E=8\hat{X}+3\hat{Y}+4\hat{Z}(\frac{N.m^2}{c})\]
(10 cm) The flux through the right side surface of a cube with edge length
equals

\[∅= 6 ×10^{-2} \;\;N.m^2/C\;\;\;\;\;\;-C\]	\[ ∅= 8 ×10^{-2 }\;\;N.m^2/C\;\;\;\;\;\;-A\]
\[∅= 2 ×10^{-2} \;\;N.m^2/C\;\;\;\;\;\;-D\]	\[∅= 4×10^{-2} \;\;N.m^2/C\;\;\;\;\;\;-B\]

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32

A hollow conducting sphere with radius \[0.2\;\;m\] was uniformly charged, losing a number of electrons equal to \[n= 5×10^{12}\] electrons. The charge density on the conductor's surface equals:
Given that \[q_e=1.6×10^{-19} c\]

\[𝛿= 1.6 ×10^{-6} \;\;c/m^2\;\;\;\;\;\;-C\]	\[𝛿= 4.8 ×10^{-6} \;\;c/m^2\;\;\;\;\;\;-A\]
\[𝛿= 3.6 ×10^{-6} \;\;c/m^2\;\;\;\;\;\;-D\]	\[𝛿= 6 ×10^{-6} \;\;c/m^2\;\;\;\;\;\;-B\]

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33

A semi-cylinder made of insulating material with small base radius (0.1 m) and large base radius (0.2 m) was placed in a uniform electric field as shown in the figure below with intensity \[500\;\;N/C\]. The flux passing through the lateral surface of the semi-cylinder equals:

\[∅=47.1 \;\;N.m^2/C\;\;\;\;\;\;-C\]	\[ ∅=0.0 \;\;\;\;\;\;-A\]
\[∅= 25.3\;\;N.m^2/C\;\;\;\;\;\;-D\]	\[∅= - 35.2 \;\;N.m^2/C\;\;\;\;\;\;-B\]

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34

A cube has a point charge at its center with a magnitude of \[8 ×10^{-9}c\]. The flux through the top and bottom surfaces is equal to \[ 𝓔_0=8.85 ×10^{-12}C.m/v\]

\[∅= 432 \;\;N.m^2/C\;\;\;\;\;\;-C\]	\[ ∅=151 \;\;N.m^2 \;\;\;\;\;\;-A\]
\[∅= 512\;\;N.m^2/C\;\;\;\;\;\;-D\]	\[∅= - 301 \;\;N.m^2/C\;\;\;\;\;\;-B\]

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Solve the following problems

1

Two point charges on a straight line each with magnitude \[q_1=8\;\;nc\;\;\;\;\;\;\;\;\;\; q_2=?\]The electric field was calculated at point \[A\] and its magnitude was \[E_{net}=500 \;\;N/C\]From the figure information and previous data What is the type of \[q_2\] \[........................................................................................\] \[........................................................................................\] \[........................................................................................\] Calculate the magnitude of charge \[q_2\] \[........................................................................................\] \[........................................................................................\] \[........................................................................................\] \[........................................................................................\] \[........................................................................................\]

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2

A pith ball with mass \[m=5 \;\;g\] is charged and suspended by an inextensible thread fixed to the ceiling. It was placed in a uniform electric field with intensity \[E=1×10^3 \;\;N/C\] causing the ball to deflect to the right as shown in the figure such that the thread makes an angle with the vertical axis of \[𝜃=8^0\] Determine the type of charge on the ball \[........................................................................................\] \[........................................................................................\] Calculate the magnitude of the ball's charge \[........................................................................................\] \[........................................................................................\] \[........................................................................................\] \[........................................................................................\] \[........................................................................................\]

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3

A spherical conductor with radius \[R=0.05 \;\; m\] has a quantity of charge distributed uniformly on its surface with surface charge density of \[𝜎=8.5\;\;nc/m^2\]Calculate the electric field at the surface of this conductor

\[........................................................................................\] \[........................................................................................\] \[........................................................................................\] \[........................................................................................\] \[........................................................................................\]

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4

A spherical shell with outer and inner radii \[R_1=0.5 \;\;m \;\;\;\;\;\;\;R_2=0.8 \;\;m \] and shell charge \[6\;\;µc\] with a charge placed at its center \[-4\;\;µc\]

Calculate the field at distance \[r_1=0.4\;\;m\] from the shell's center \[...................................\;\;\;\;\;\;\;...................................\] \[...................................\;\;\;\;\;\;\;...................................\]\[...................................\;\;\;\;\;\;\;...................................\] Calculate the field at distance \[r_2=0.7\;\;m\] from the shell's center \[...................................\;\;\;\;\;\;\;...................................\] \[...................................\;\;\;\;\;\;\;...................................\]\[...................................\;\;\;\;\;\;\;...................................\] Calculate the field at distance \[r_3=1\;\;m\] from the shell's center \[...................................\;\;\;\;\;\;\;...................................\] \[...................................\;\;\;\;\;\;\;...................................\]\[...................................\;\;\;\;\;\;\;...................................\]

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5

A cube with side length \[0.3\;\;m\]
was placed in a uniform electric field directed towards the positive horizontal axis
with intensity \[E=200\frac{N}{C}\] Calculate the flux through each surface and the total flux

\[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] A point charge was placed at the center of the previous cube inside the electric field region with magnitude \[q=20 \;\;pc\] Calculate the flux through the left side surface \[𝜺_𝟎=8.85 ×10^{-12}\;\;\frac{c^2}{N.m^2}\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\]

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6

A cube containing 12 protons, 13 neutrons, and some electrons
The measured electric flux through the cube was \[∅=9.05×10^{-8}\;N.m^2/c\] Calculate the magnitude of charge inside the cube Given that \[𝜀_0=8.85×10^{−12}\;c^2/N.m^2\]

\[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] Calculate the number of electrons inside the cube \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\]

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