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<<< Question Bank: Electric Potential and Potential Energy >>>

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\[1 \star\]

The electric potential energy of a positive charge increases when it moves

Perpendicular to the field -C

In the direction of the field -A

In the direction of the electric force -D

Opposite to the field -B

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    \[2 \star\]

    A positive charge (proton) is moved between two points \[A\;\;\Rightarrow\;\;B\] Coordinates of the points: \[A=(2\;m,-3\;m)\;\;\;\;\;\;\;B=(-2\;m,2\;m)\] In a uniform electric field of intensity: \[E=4× 10^3\;\;N/C\]
    Directed toward the negative vertical axis as shown below. The change in electric potential energy equals:
    \[ q_p = 1.6 ×10^{-19}C\]

    \[∆ 𝑈= - 2.56 × 10^{-15}\;\; J \;\;\;\;\;\;-C\]

    \[ ∆ 𝑈= 3.2 × 10^{-15}\;\; J \;\;\;\;\;\;-A\]

    \[∆ 𝑈= - 3.2 × 10^{-15}\;\; J \;\;\;\;\;\;-D\]

    \[ ∆ 𝑈= 2.56 × 10^{-15}\;\; J \;\;\;\;\;\;-B\]

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    \[3\star\]

    A capacitor with plates has an electric field intensity between them of: \[E=500 \;\;N/C\] and the distance between them is \[15\;\;Cm\] as shown below. The electric potential energy of an electron at a point 5 cm from the negative plate equals: \[q_e=-1.6 × 10^{-19}\;\;c\]

    \[u= 4 × 10^{-18}\;\;J \;\;\;\;\;\;-C\]

    \[u= 1.2 × 10^{-17}\;\;J \;\;\;\;\;\;-A\]

    \[u= 0.6 × 10^{-17}\;\;J\;\;\;\;\;\;-D\]

    \[u= 8 × 10^{-18}\;\;J\;\;\;\;\;\;-B\]

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    \[4 \star \star\]

    An electron and proton are separated by \[2\;\;𝝁m\] The work done to increase the distance between them to \[4\;\;Cm\]

    \[ W = -1.15 × 10^{-22}\;\;J \;\;\;\;\;\;-C\]

    \[W = -4.24 × 10^{-22}\;\;J \;\;\;\;\;\;-A\]

    \[W = 3.64 × 10^{-22}\;\;J\;\;\;\;\;\;-D\]

    \[ W = 2.25 × 10^{-22}\;\;J\;\;\;\;\;\;-B\]

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    \[5 \star \]

    An electron moved between two points in an electric field. If it started with a velocity of \[A\Rightarrow\;\;v_A=80 \frac{m}{s}\] and its velocity at point B became \[B\Rightarrow\;\;v_B=10^5\frac{m}{s}\] Calculate the potential difference between the two points given that \[q_e= - 1.6×10^{-19}C , m_e=9.1×10^{-31}kg\]

    \[ ∆𝑉=- 0.03\;\; V \;\;\;\;\;\;-C\]

    \[∆𝑉= 0.01\;\; V \;\;\;\;\;\;-A\]

    \[ ∆𝑉= -0.04\;\; V \;\;\;\;\;\;-D\]

    \[ ∆𝑉= 0.02\;\; V \;\;\;\;\;\;-B\]

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    \[6 \star\]

    A proton was allowed to move between two points with a potential difference of \[∆𝑉= 500\;\; V \]The final velocity of the proton equals Given that \[q_P= 1.6×10^{-19}C , m_P=1.67×10^{-27}kg\]

    \[𝑣_𝑓=1.2 × 10^5 \;\;m/s \;\;\;\;\;\;-C\]

    \[𝑣_𝑓=5.2 × 10^5 \;\;m/s \;\;\;\;\;\;-A\]

    \[ 𝑣_𝑓=1.8 × 10^5 \;\;m/s \;\;\;\;\;\;-D\]

    \[ 𝑣_𝑓=3.1 × 10^5 \;\;m/s \;\;\;\;\;\;-B\]

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    \[7 \star\]

    \[A\;\;\;,B\]Two points inside an electric field \[V_A= 100 V , V_B=60 V \]A proton was moved from point \[A\Rightarrow B \] Then one of the following answers correctly expresses the movement of the proton in the field

    \[ ΔU = 6.4 × 10^{-18}\;\;J \;\;\;\;\;\;-C\]

    \[ΔK= 6.4 × 10^{-18}\;\;J \;\;\;\;\;\;-A\]

    \[W = 3.64 × 10^{-22}\;\;J\;\;\;\;\;\;-D\]

    \[ ΔV_(AB)=40\;\;V\;\;\;\;\;\;-B\]

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    \[8 \star \star\]

    The potential at point A was calculated
    \[A\;\;\;\; V_A= -45 V \] and the field at the same point was calculated to be \[E=112.5 \;\;N/C\] Then the magnitude and type of charge affecting that point equals

    \[q= -2 × 10^{-9}\;\;C\;\;\;\;\;\;-C\]

    \[q= 4 × 10^{-9}\;\;C \;\;\;\;\;\;-A\]

    \[q= -4 × 10^{-9}\;\;C\;\;\;\;\;\;-D\]

    \[ q= 2 × 10^{-9}\;\;C\;\;\;\;\;\;-B\]

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    \[9 \star \star\]

    In the figure below, an electron was transferred from point \[A\Rightarrow B \] The work done equals
    Given that \[q_e= - 1.6×10^{-19}C \]

    \[q= W= 4.32 × 10^{-17}\;\;J\;\;\;\;\;\;-C\]

    \[ W= - 4.32 × 10^{-17}\;\;J \;\;\;\;\;\;-A\]

    \[ W= 5.32 × 10^{-17}\;\;J\;\;\;\;\;\;-D\]

    \[ W= -5.32 × 10^{-17}\;\;J\;\;\;\;\;\;-B\]

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    \[10 \star \star\]

    In the figure below, there are two charges: \[q_1= -4 \;\;nC\;\;\;,\;\;\;q_2=6\;\;nC\] The first charge is negative and placed at the origin point, and the second charge is positive and placed at a point \[0.4\;\;m\] away from the origin. The point of zero potential on the line connecting the two charges is located at position:

    \[ X=0.14 \;\;m \;\;\;\;\;\;-C\]

    \[ X=0.12 \;\;m \;\;\;\;\;\;-A\]

    \[ X=0.18\;\; m\;\;\;\;\;\;-D\]

    \[ X=0.16\;\; m \;\;\;\;\;\;-B\]

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    \[11 \star \star \star\]

    For a parallel plate capacitor, the potential difference between the plates is \[ ∆𝑉= 150 \;\; V\] and the distance between the plates is \[6\;\;Cm\] then the potential at a point located at a distance from the positive plate \[X_A= 2\;\; Cm \] equals

    \[VA=50\;\; V\;\;\;\;\;\;-C\]

    \[VA=120\;\; V \;\;\;\;\;\;-A\]

    \[ VA=100\;\; V\;\;\;\;\;\;-D\]

    \[ VA=80\;\; V\;\;\;\;\;\;-B\]

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    \[12 \star \star\]

    In the figure below, a uniform field with intensity \[ E = 500 \;\;N/C \] then the potential difference between points \[∆𝑉_{𝐴𝐵}=?\] and the dimensions are shown in the figure equals

    \[∆𝑉(𝐴𝐵)=-200\;\; V\;\;\;\;\;\;-C\]

    \[∆𝑉(𝐴𝐵)=-150\;\; V \;\;\;\;\;\;-A\]

    \[ ∆𝑉(𝐴𝐵)=200\;\; V\;\;\;\;\;\;-D\]

    \[ ∆𝑉(𝐴𝐵)=150\;\; V\;\;\;\;\;\;-B\]

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    \[13 \star\]

    Three points inside a uniform field as shown in the figure below, one of the lines represents the correct shape of the uniform field lines given that \[ 0 > ∆𝑉_{𝐴𝐵} , ∆𝑉_{𝐴C}= 0\]

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    \[14 \star \star\]

    A charged particle was moved from point \[A\Rightarrow B\] The work done to move the charged particle is:

    \[0>W\;\;\;\;\;\;-C\]

    \[ W>0 \;\;\;\;\;\;-A\]

    Cannot determine work because the particle's charge is unknown -D

    \[ W=0\;\; V\;\;\;\;\;\;-B\]

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    \[15 \star\]

    The figure below shows equipotential surface lines. The maximum electric field magnitude
    at point \[K\] in the figure

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    \[16 \star \star\]

    A uniformly charged wire with linear charge density \[ λ= 4×10^{-8}\;\;C/m\] is bent into a quarter-circle of radius R. The potential at the center of curvature is: \[R\]

    \[V=565.5 \;\;V\;\;\;\;\;\;-C\]

    \[ V=322.2 \;\; V \;\;\;\;\;\;-A\]

    \[ V=630.4\;\;V\;\;\;\;\;\;-D\]

    \[ V=1131\;\; V\;\;\;\;\;\;-B\]

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    \[17 \star \star \star\]

    The electric potential in a region of space is given by the relation: \[V(X,Y,Z)=5X^2+8XY+7Z\] The value of the electric field at a point with coordinates \[(5,-2,-3)\] equals:

    \[E =67.2\;\; N/C\;\;\;\;\;\;-C\]

    \[E =52.9\;\; N/C \;\;\;\;\;\;-A\]

    \[ E =32.8 \;\;N/C \;\;\;\;\;\;-D\]

    \[ E =64.5 \;\;N/C\;\;\;\;\;\;-B\]

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    \[18 \star \star \star\]

    A small charged body with charge \[ 3 \;\;µC\] placed at point \[ X= 1\;\; m \] in a region where the electric potential varies according to the relation \[ V_{x}= 4-3X^3\] then the electric force acting on the particle equals

    \[F= 6.5 × 10^{-5}\;\;N\;\;\;\;\;\;-C\]

    \[F= 3.6 × 10^{-5}\;\;N \;\;\;\;\;\;-A\]

    \[F= 4.5 × 10^{-5}\;\;N\;\;\;\;\;\;-D\]

    \[ F=2.7 × 10^{-5}\;\;N\;\;\;\;\;\;-B\]

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    \[19 \star \star \star\]

    In the figure below, three equal magnitude charges are placed \[q_1=q_2=q_3=2\;\;nC\]
    on the vertices of a right-angled triangle with dimensions shown in the drawing then the work done to bring the charge at the right angle vertex from infinity to its current position equals

    \[𝑊=- 7.1 × 10^{-7}\;\;J\;\;\;\;\;\;-C\]

    \[𝑊=+ 5.2 × 10^{-7}\;\;J\;\;\;\;\;\;-A\]

    \[𝑊=- 2.1 × 10^{-7}\;\;J\;\;\;\;\;\;-D\]

    \[ 𝑊=+3.6 × 10^{-7}\;\;J\;\;\;\;\;\;-B\]

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    \[20 \star \star\]

    Three charges located at the vertices of a right-angled triangle as shown in the figure below \[q_1=-8\;\;nc\;\;\;q_2=-6\;\;nc\;\;\;q_3=3\;\;nc\]


    Then the potential energy of the system consisting of three charges

    \[ U=+2.85 × 10^{-7}\;\;J\;\;\;\;\;\;-C\]

    \[ U=+5.67 × 10^{-7}\;\;J\;\;\;\;\;\;-A\]

    \[ U=+7.44 × 10^{-7}\;\;J\;\;\;\;\;\;-D\]

    \[ U=+3.45 × 10^{-7}\;\;J\;\;\;\;\;\;-B\]

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    \[21 \star\]

    A spherical conductor with radius \[R=0.5\;\;m\] and the field strength on the conductor's surface equals \[ E=5000 \;\;N/C\] then the potential at a point distant from the conductor's center \[0.2\;\;m\]equals

    \V=2500 \;\;V\;\;\;\;\;\;-C\]

    \[ V=0.0 \;\; V \;\;\;\;\;\;-A\]

    \[ V= V=1500\;\;V\;\;\;\;\;\;-D\]

    \[ V=10000\;\; V\;\;\;\;\;\;-B\]

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    \[22 \star \star \star\]

    The following figure represents the electric potential as a function of the horizontal axis coordinates
    The correct drawing of the corresponding electric field as a function of the horizontal axis

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    \[23 \star\]

    An electric charge \[Q\]was placed at the origin. What is the ratio of the absolute potential at point \[A\]to the absolute potential at point \[B\]

    \[ 0.33 \;\;\;\;\;\;-C\]

    \[ 0.5 \;\;\;\;\;\;-A\]

    \[ 3\;\;\;\;\;\;-D\]

    \[ 2 \;\;\;\;\;\;-B\]

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    \[24 \star\]

    Two points \[A\;\;\;,B\] are at a distance \[r\] from two unequal charges, \[-Q\;\;\;\;+3Q\]. The work required to move a charge \[q\] from point \[A\Rightarrow B\]

    \[ W>0.0 \;\;\;\;\;\;-C\]

    Depends on the path taken-A

    \[ 0.0>W\;\;\;\;\;\;-D\]

    \[ W=0.0\;\;\;\;\;\;-B\]

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    \[25 \star \star\]

    An electric field is created by a positive charge
    .The distribution of electric field lines and equipotential lines is shown in the diagram
    .Which of the following statements is correct regarding the electric potential?

    \[ 𝑉_𝐴>𝑉_𝐵=𝑉_𝐶>𝑉_𝐷\;\;\;\;\;\;-C\]

    \[ 𝑉_D>𝑉_𝐵>𝑉_𝐶>𝑉_A \;\;\;\;\;\;-A\]

    \[𝑉_D>𝑉_𝐵=𝑉_𝐶>𝑉_A\;\;\;\;\;\;-D\]

    \[ 𝑉_𝐴>𝑉_𝐵>𝑉_𝐶>𝑉_𝐷\;\;\;\;\;\;-B\]

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    \[26 \star \star\]

    Four equal negative charges each of magnitude \[-q\] are arranged as shown in the figure
    Calculate the net electric potential at the center of the square?


    \[ V_{net}=-4\sqrt 2\frac {k.q}{r} \;\;\;\;\;\;-C\]

    \[ V_{net}=-\sqrt 2\frac {k.q}{r} \;\;\;\;\;\;-A\]

    \[ V_{net}=0\;\;\;\;\;\;-D\]

    \[ V_{net}=-2\sqrt 2\frac {k.q}{r}\;\;\;\;\;\;-B\]

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    \[27 \star\]

    A point charge \[q_1=+6.0\;\; µC \] is placed at point \[-3\;\;m\] and a second charge \[q_2=?\] is placed at point \[2\;\;m\]. The net electric potential at the origin is zero.
    Then the magnitude and type of charge \[q_2\] equals

    \[q_2= 5 \times 10^{-6}\;\;C \;\;\;\;\;\;-C\]

    \[q_2= -4 \times 10^{-6}\;\;C \;\;\;\;\;\;-A\]

    \[q_2= 4 \times 10^{-6}\;\;C \;\;\;\;\;\;-D\]

    \[q_2= -5 \times 10^{-6}\;\;C \;\;\;\;\;\;-B\]

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    Solve the following problems

    \[1 \star\]

    A uniform field with intensity \[E=3×10^3\;\;N/c\] as shown in the figure below

    Arrange points \[A,B.C\] from highest to lowest potential \[.....................................\;\;\;\;............................................\] An electron is allowed to move from \[A\Rightarrow B\] using the figure Calculate the electron's velocity when it reaches point \[B\] \[q_e=-1.6×10^{-19}\;\;c\;\;\;\;\;\;\;\;m_e=9.1×10^{-31}\;\;kg\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] Calculate the electron's acceleration and determine if it's uniform or non-uniform and explain why \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\]
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  • \[2 \star\]

    The figure represents electric potential as a function of horizontal axis coordinates Based on the figure's information

    Calculate the change in potential energy for a proton moving from position \[0\Rightarrow 10\;\;cm\] \[q_p=+1.6×10^{-19}\;\;c\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] Calculate the electric field from position \[10\;\;cm\Rightarrow 16\;\;cm\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\]
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  • \[3 \star\]

    Three point charges with same magnitude but different types are shown in the figure below

    Draw equipotential lines
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  • \[4 \star\]

    A small object with charge \[ 3 \;\;µC\] placed at point \[ X= 2\;\; m \] in a region where electric potential varies according to the relation \[ V_{x}= 4X-2X^3\] Calculate the potential at point \[X\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] Calculate the field at the same point \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] Calculate the electric force acting on the particle \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\]

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  • \[5 \star\]

    A small object with charge \[ 6 \;\;µC\] placed at point \[A= ( 4\widehat X\;\; m \;\;\;,\;\;\;-2\widehat Y \;\;m)\] in a region where electric potential varies according to the relation \[ V= 3X^2.Y^3-2X^3.Y^2+10\] Calculate the potential at point \[A\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] Calculate the field at the same point \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] Calculate the electric force acting on the particle \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\]

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  • \[6 \star\]

    A parallel plate capacitor connected to a battery with constant voltage \[v=120\; v\] Each plate has length \[0.35\;m\] separated by distance \[0.05 \;m\] An electron moves with initial horizontal velocity \[v=2.9 ×10^7\;\;m/s\] and enters the space between plates at the midpoint. Ignore gravity. Will the electron leave the space between the plates? Note: \[q_e=1.6×10^{-19}\;\;c\;\;\;\;\;\;\;\; m_e=9.1×10^{-31}\;\;kg\]

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