(b) ?What is the potential difference, VC – ?VA? ?Here, VC is the electric potential at C and VA is the electric potential at A. [1 ?point]
(c) ?What is the change in electric potential energy of a charge q = 10 ?nC when it is moved along path a from A to B? [1 ?point]
(d) ?What is the change in electric potential energy of a charge q = 10 ?nC when it is moved along path b from A to D? [1 ?point]
(e) ?What is the change in electric potential energy of a charge q = 10 ?nC when it is moved
The correct answer and explanation is:
Let’s break down each part of the question:
(b) What is the potential difference, VC−VAV_C – V_A?
The potential difference between points C and A, denoted as VC−VAV_C – V_A, refers to the difference in electric potential between the two locations. The potential difference is related to the electric field and the distance between the points. If the electric field is constant, the potential difference can be calculated using: VC−VA=−∫ACE⋅drV_C – V_A = – \int_A^C \mathbf{E} \cdot d\mathbf{r}
Where:
- E\mathbf{E} is the electric field vector
- drd\mathbf{r} is a differential displacement along the path from A to C
- The negative sign indicates that the potential decreases in the direction of the electric field.
If the electric field and path are known, you can calculate the potential difference.
(c) What is the change in electric potential energy of a charge q=10 nCq = 10 \, \text{nC} when it is moved along path a from A to B?
The change in electric potential energy of a charge qq when it is moved between two points with potentials VAV_A and VBV_B is given by: ΔU=q(VB−VA)\Delta U = q (V_B – V_A)
Substituting q=10 nCq = 10 \, \text{nC}, you need the potential difference between points A and B to calculate the change in potential energy.
(d) What is the change in electric potential energy of a charge q=10 nCq = 10 \, \text{nC} when it is moved along path b from A to D?
Similarly, the change in electric potential energy when the charge q=10 nCq = 10 \, \text{nC} is moved from A to D is: ΔU=q(VD−VA)\Delta U = q (V_D – V_A)
Again, you need the electric potential at point D, VDV_D, to compute the change in energy.
(e) What is the change in electric potential energy of a charge q=10 nCq = 10 \, \text{nC} when it is moved?
In this case, the change in electric potential energy depends on the path and the electric potentials at the starting and ending points. The general formula remains: ΔU=q(Vfinal−Vinitial)\Delta U = q (V_{\text{final}} – V_{\text{initial}})
If the path is along a specific route, you would apply the potential difference along that route.
Explanation
The electric potential energy of a charge in an electric field depends on the potential at a given point in space. The potential difference between two points is the key factor in determining the change in electric potential energy when a charge moves between those points.
The electric potential at a point is a scalar quantity that represents the potential energy per unit charge at that point due to the electric field. The potential difference between two points, such as A and B, can be defined as: VB−VA=UB−UAqV_B – V_A = \frac{U_B – U_A}{q}
Where UBU_B and UAU_A are the electric potential energies at points B and A, respectively, and qq is the charge. The change in electric potential energy of a charge qq when it moves between two points is simply the charge multiplied by the potential difference between those points: ΔU=q(Vfinal−Vinitial)\Delta U = q (V_{\text{final}} – V_{\text{initial}})
This formula holds true irrespective of the path the charge takes, as long as the electric field is conservative (which is usually the case in electrostatic situations). The work done in moving the charge along a path is equal to the negative of the change in electric potential energy, and this work does not depend on the path if the field is conservative.
If you know the values of electric potential at various points (like A, B, C, and D), you can substitute them into these formulas to find the changes in electric potential energy for different paths.