What are the strength and direction of the electric field at the position indicated by the dot in the diagram below, in which d = 4.9 cm, q = 11 nC, the positive x-axis points to the right, and the positive y-axis points up? Give your answer in each of the following forms.
The diagram is a rectangle with corners from top left to bottom left clockwise: the point, q, q, -5 nC. The rectangle has a lenth of d and a width of 2.0 com.
To find the strength and direction of the electric field at the position indicated by the dot in the diagram, we can use Coulomb's Law.
Coulomb's Law states that the electric field created by a point charge is given by the formula:
E = k * (q / r^2)
Where:
E is the electric field strength,
k is Coulomb's constant (9 x 10^9 N m^2 / C^2),
q is the charge,
and r is the distance from the charge to the point where we want to find the electric field.
In this case, the point charge q = 11 nC, and the distance from the charge to the point we are interested in is d = 4.9 cm.
First, we need to convert the distance from centimeters to meters:
d = 4.9 cm = 0.049 m
Now, we can calculate the electric field strength at the point indicated by the dot:
E = (9 x 10^9 N m^2 / C^2) * (11 x 10^-9 C) / (0.049 m)^2
Simplifying the calculation:
E = (9 x 10^9 N m^2 / C^2) * (11 x 10^-9 C) / (0.049)^2 m^2
E = (9 x 11 x 10^9 x 10^-9 N m^2) / (0.049)^2 C m^2
E = 99 x 10^9 N / (0.049)^2 C
Now, let's calculate the value:
E = 99 x 10^9 N / (0.049)^2 C
E = 99 x 10^9 N / 0.002401 C
E = 4.121 x 10^13 N/C
So, the electric field strength at the position indicated by the dot in the diagram is approximately 4.121 x 10^13 N/C.
To find the direction of the electric field, we can use the principle that positive charges repel each other and negative charges attract positive charges.
In the diagram, there are two positive charges (q) and one negative charge (-5 nC) surrounding the dot. Since positive charges repel each other, the electric field at the dot will point away from the positive charges.
Therefore, the electric field at the position indicated by the dot points away from the rectangle.