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At one point in space, the electric potential energy of a 15 nC charge is 42 μJ . Part A) What is the electric potential at this point?
Express your answer to two significant figures and include the appropriate units.

Part B) If a 20 nC charge were placed at this point, what would its electric potential energy be?
Express your answer to two significant figures and include the appropriate units.

Respuesta :

Answer:

Part A:

[tex]\rm 2.8\times 10^3\ Volts.[/tex]

Part B:

[tex]\rm 5.6\times 10^{-5}\ J.[/tex]

Explanation:

Part A:

  • Potential energy of charge at the given point, [tex]\rm U=42\ \mu J=42\times 10^{-6}\ J.[/tex]
  • Charge, [tex]\rm q=15\ nC = 15\times 10^{-9}\ C.[/tex]

The potential energy at a point due to a charge is defined as

[tex]\rm U=qV[/tex].

where,

V = electric potential at that point.

Therefore,

[tex]\rm V=\dfrac{U}{q}=\dfrac{42\times 10^{-6}}{15\times 10^{-9}}=2.8\times 10^3\ Volts.[/tex]

Part B:

Now, if the charge at that point is replaced with [tex]\rm q_1 = 20\ nC = 20\times 10^{-9}\ C.[/tex], then the electric potential energy at that point is given by

[tex]\rm U=q_1V = 20\times 10^{-9}\times 2.8\times 10^3=5.6\times 10^{-5}\ J.[/tex]

Electric potential energy is the energy which is required to move a unit charge from a point to another point in the electric field.

  • a) The electric potential at this point when 15 nC charge is placed at one point in space is [tex]2.8\times10^3[/tex] V.
  • b) The electric potential energy, when 20 nC charge is placed at one point in space is [tex]5.6\times10^{-5}[/tex] J.

What is electric potential energy?

Electric potential energy is the energy which is required to move a unit charge from a point to another point in the electric field.

It can be given as,

[tex]U=qV[/tex]

Here, [tex]q[/tex] is the charge and [tex]V[/tex] is the electric potential.

Thus the electric potential can be given as,

[tex]V=\dfrac{U}{q}[/tex]

Given information-

The value of electric potential energy is 42 μJ.

  • a) The electric potential at this point when 15nC charge is placed at one point in space.

As the value of electric potential energy is 42 μJ and charge is 15 nC. Then using the above formula,  the electric potential can be given as,

[tex]V=\dfrac{42\times10^{-6}}{15\times10^{-9}}\\V=2.8\times10^3\rm volts[/tex]

Thus the value of electric potential is [tex]2.8\times10^3[/tex] V.

  • b) The electric potential energy, when 20 nC charge is placed at one point in space.

As the value of electric potential is [tex]2.8\times10^3[/tex] V and charge is 20 nC. Then using the above formula,  the electric potential can be given as,

[tex]U=({2.8\times10^{3})}\times({20\times10^{-9}})\\V=5.6\times10^{-5}\rm J[/tex]

Thus the value of electric potential energy is [tex]5.6\times10^{-5}[/tex] J.

Hence,

  • a) The electric potential at this point when 15 nC charge is placed at one point in space is [tex]2.8\times10^3[/tex] V.
  • b) The electric potential energy, when 20 nC charge is placed at one point in space is [tex]5.6\times10^{-5}[/tex] J.

Learn more about the electric potential energy here;

https://brainly.com/question/14306881

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