A point charge q1 = –7 nC is at the point x1 = 0.6m, y1 = 0.8
m, and a second point charge q2 = 4 nC is at the point,. Find
the magnitude and direction of the net electric field at the origin.
x2 = 0.6 m and y2 = 0m
E=540N
find the magnitude and direction of the net electric field at the origin X2=0.6mand y=0m
To find the net electric field at the origin (0, 0), we need to calculate the electric fields due to each point charge and then add them vectorially.
The electric field due to a point charge q at a distance r is given by:
E = k * |q| / r^2
where k is the electrostatic constant (k = 9 x 10^9 N m^2/C^2).
First, let's calculate the electric field due to q1 at the origin.
Distance from q1 to the origin:
r1 = √((x1 - x)^2 + (y1 - y)^2)
= √((0.6m - 0m)^2 + (0.8m - 0m)^2)
= √(0.36m^2 + 0.64m^2)
= √(1m^2)
= 1m
Electric field due to q1 at the origin:
E1 = k * |q1| / r1^2
= (9 x 10^9 N m^2/C^2) * (7 x 10^-9 C) / (1m)^2
= 63 N/C
Now let's calculate the electric field due to q2 at the origin.
Distance from q2 to the origin:
r2 = √((x2 - x)^2 + (y2 - y)^2)
= √((0.6m - 0m)^2 + (0m - 0m)^2)
= √(0.36m^2 + 0m^2)
= √(0.36m^2)
= 0.6m
Electric field due to q2 at the origin:
E2 = k * |q2| / r2^2
= (9 x 10^9 N m^2/C^2) * (4 x 10^-9 C) / (0.6m)^2
= 266.67 N/C
Since the two electric fields are in the same direction (along the positive x-axis), we can simply add them together to determine the net electric field at the origin:
Net electric field at the origin:
E_net = E1 + E2
= 63 N/C + 266.67 N/C
≈ 329.67 N/C
Therefore, the magnitude of the net electric field at the origin is approximately 329.67 N/C.
Since both electric fields are along the positive x-axis, the direction of the net electric field at the origin is also along the positive x-axis.
To find the magnitude and direction of the net electric field at the origin (0,0), we can follow these steps:
Step 1: Calculate the electric field due to each charge separately using the formula for the electric field of a point charge:
Electric Field due to q1 = k * q1 / r1^2
Electric Field due to q2 = k * q2 / r2^2
Here,
k = Coulomb's constant = 9 x 10^9 Nm^2/C^2
q1 = -7 nC = -7 x 10^-9 C
q2 = 4 nC = 4 x 10^-9 C
r1 = distance from q1 to the origin = sqrt(x1^2 + y1^2)
r2 = distance from q2 to the origin = sqrt(x2^2 + y2^2)
Step 2: Calculate the components of each electric field using Cartesian coordinates:
Electric Field components in x-direction:
Ex1 = Electric Field due to q1 * cos(theta1)
Ex2 = Electric Field due to q2 * cos(theta2)
Electric Field components in y-direction:
Ey1 = Electric Field due to q1 * sin(theta1)
Ey2 = Electric Field due to q2 * sin(theta2)
Here,
theta1 = angle made by the line connecting q1 and the origin with the x-axis = atan(y1/x1)
theta2 = angle made by the line connecting q2 and the origin with the x-axis = atan(y2/x2)
Step 3: Calculate the net electric field components by adding the components from each charge:
Ex_net = Ex1 + Ex2
Ey_net = Ey1 + Ey2
Step 4: Calculate the magnitude and direction of the net electric field at the origin:
Magnitude of the net electric field at the origin:
E_net = sqrt(Ex_net^2 + Ey_net^2)
Direction of the net electric field at the origin:
theta_net = atan(Ey_net/Ex_net)
By following these steps and plugging in the given values, you can find the magnitude and direction of the net electric field at the origin.