A uniform electric field of magnitude 75 n/c is created at an angle of 33 degree relative to the positive x-axis.
a)Find the voltage between the points (0.5m,0)& (0,0).
b)find the value of y such that the voltage between the points (0.3 m, y) and (0,0) has the same value as in part (a).
c) Plot all points (x,y) which are such that the voltage between (x,y) and (0,0) has the same value as part(a).
To solve these problems, we will use the formula for the electric potential created by a uniform electric field: V = Ed, where V is the voltage, E is the electric field magnitude, and d is the distance.
a) To find the voltage between the points (0.5m,0) and (0,0):
We are given the magnitude of the electric field, E = 75 n/C, and the distance, d = 0.5 m.
Since the electric field and the distance are parallel to each other, the angle between them is 0 degrees.
Using the formula V = Ed, we can calculate:
V = (75 n/C)(0.5 m) = 37.5 V
Therefore, the voltage between the points (0.5m,0) and (0,0) is 37.5 volts.
b) To find the value of y such that the voltage between the points (0.3 m, y) and (0,0) has the same value as in part (a):
We need to find a point (0.3 m, y) where the distance from (0.3 m, y) to (0,0) is the same as the distance from (0.5 m, 0) to (0,0) in part (a).
Let's call this distance D. Since points (0.3 m, y) and (0.5 m, 0) lie on the same line with the same slope (given by the electric field angle), we can use similar triangles to find the value of y.
The ratio of the distances between these points and the origin is given by:
(0.3 - 0) / D = (0.5 - 0) / 0.5
0.3 / D = 1 / 0.5
0.3D = 1 * D
0.3D = D
0.3 = 1
D = 0.3 m
Therefore, the distance between (0,0) and (0.3 m, y) is 0.3 m.
Now, we can use the formula V = Ed to solve for y:
V = Ed
37.5 = (75 n/C)(0.3 m)
37.5 = 22.5 n*m/C
1.67 = n*m/C
Therefore, the value of y such that the voltage between the points (0.3 m, y) and (0,0) has the same value as in part (a) is approximately 1.67 C.
c) To plot all points (x,y) which have the same voltage as in part (a):
We can plot a graph with x on the x-axis and voltage (V) on the y-axis.
- Set up the x-axis with a suitable range based on the given information.
- For each x-coordinate, calculate the voltage using the formula V = Ed.
- Plot the corresponding point (x, V).
- Connect all the plotted points to generate the graph.
By following these steps, you will obtain a graph that represents all points (x,y) satisfying the condition from part (a).