Three charges are placed on the vertices of an equilateral triangle whose side is 0.025 m. Find the net electric field at the center of the base of the triangle (point P). q1= - 3.0 mC , q2= -2.0 nC , q3= +4.0 nC.
ano po sagot?
To find the net electric field at point P, you need to calculate the electric fields created by each charge and then add them up vectorially.
The electric field created by a point charge is given by Coulomb's law:
E = (k * q) / r^2
where E is the electric field, k is the electrostatic constant (8.99 x 10^9 N*m^2/C^2), q is the charge, and r is the distance between the charge and the point where you want to calculate the electric field.
Let's calculate the electric fields created by each charge.
For q1 = -3.0 mC, the electric field created at point P is given by:
E1 = (k * q1) / r1^2
where r1 is the distance between q1 and point P. Since the triangle is equilateral, the distance between q1 and point P is half the length of the side of the triangle:
r1 = 0.025 m / 2 = 0.0125 m
Substituting the values into the equation:
E1 = (8.99 x 10^9 N*m^2/C^2 * (-3.0 x 10^-3 C)) / (0.0125 m)^2
Calculate the value of E1.
Next, calculate the electric field created by q2 = -2.0 nC:
r2 = 0.025 m (since q2 is on the base of the triangle)
E2 = (k * q2) / r2^2
Substituting the values into the equation:
E2 = (8.99 x 10^9 N*m^2/C^2 * (-2.0 x 10^-9 C)) / (0.025 m)^2
Calculate the value of E2.
Lastly, calculate the electric field created by q3 = +4.0 nC:
r3 = 0.025 m (since q3 is also on the base of the triangle)
E3 = (k * q3) / r3^2
Substituting the values into the equation:
E3 = (8.99 x 10^9 N*m^2/C^2 * (4.0 x 10^-9 C)) / (0.025 m)^2
Calculate the value of E3.
Once you have calculated the electric fields E1, E2, and E3, you can find the net electric field at point P by adding them up vectorially. Since all three charges are on the base of the triangle, the electric fields they create will have the same direction (towards point P). Therefore, you can simply add the magnitudes of the electric fields:
net electric field at P = E1 + E2 + E3