Respuesta :
Answer:
(a) Ey is negative
(b) The magnitude of the electric field is E = 171.429 V/m
(c) The potential difference between points B and C is 17.1429 V
Explanation:
(a) Here, we have the potentials given by;
[tex]V_A - V_B = +12.0V[/tex] with point A at y = 8.00 cm and point B at point y = 15.0 cm
where point B is at a higher potential than point A, that is the electric potential is from;
B with y = 15.0 cm to A with y = 8.0 cm which means
[tex]E_y[/tex] decreases as y increases or [tex]E_y[/tex] is negative.
(b) The magnitude of the electric field is given by
The work done to move a charge from B to A is
[tex]W_{BA} = - \Delta U[/tex] where
[tex]\Delta U = U_a -U_b = q_0E(y_b-y_a)[/tex]
[tex]V_{BA} = \frac{\Delta U}{q_0} = \frac{q_0E(y_b-y_a)}{q_0} = E(y_b-y_a)[/tex]
∴ [tex]E = \frac{V_{BA}}{(y_b-y_a)}[/tex]
[tex]E = \frac{12 \hspace{0.09cm}V}{(0.015\hspace{0.09cm} m -0.008\hspace{0.09cm} m)}[/tex]
E = 171.429 V/m
(c) Here we have point C x = 5.00 cm and y = 5.00 cm
Therefore we have the distance from B to C given by
[tex]y_b-y_c = 15.00 \hspace{0.09cm}cm - 5.00 \hspace{0.09cm}cm = 10.00 \hspace{0.09cm} cm[/tex]
Where 10.00 cm = 0.01 m
E = V/Δy
Therefore, V = Δy·E
For [tex]V_{BC}[/tex], Δy = [tex]y_b-y_c = 0.01 \hspace{0.09cm} m[/tex] and we have,
[tex]V_{BC} = E\times (y_b-y_c)[/tex]
[tex]V_{BC} = 171.429\times (0.015-0.005) = 17.1429\hspace{0.09cm}V[/tex]
(a) The electric field is negative.
(b) The magnitude of the electric field is 1.71 V/m
(c) The potential difference between point B and C is 17.1 V
Given that the electric field has only y-component. Point A and B are at 8cm and 15 cm respectively on y-axis.points
Potential Difference:
(a) The potential difference is given by:
[tex]E=-\frac{\Delta V}{\Delta r}[/tex]
Here [tex]\Delta V[/tex] is positive and [tex]\Delta r=15-8=7cm[/tex] is also positive, therefore [tex]E[/tex]must be negative.
(b)The magnitude of the electric field:
[tex]E=-\frac{\Delta V}{\Delta r}=-\frac{12}{7}V/m=-1.71V/m[/tex]
Thus the magnitude of the electric field is 1.71 V/m
(c) Only the Y coordinate of point C will be considered since the electric field is in y-direction only.
So, [tex]\Delta V_{BC}=-E\Delta r=-(-1.71)(15-5)V=17.1 V[/tex]
Learn more about potential difference:
https://brainly.com/question/1313684?referrer=searchResults
