A point charge Q1=-2 microcoulomb is located at x=0, and a point charge Q2=+8 microcoulomb, is placed at x=-0.5 on the x axis of a cartesian coordinate system.The goal of this problem is to determine the electric field,at various points along the x axis.
a)What is electric field (in N/C) for
-55.0 m ?
b)What is electric field (in N/C) at -0.22 m?
c)What is electric field (in N/C) at 92 m?
d)At what point (apart from x=infinite), is the electric field zero ? Express your answer in meters.
To determine the electric field at different points along the x-axis, we can use Coulomb's law which states that the electric field, E, created by a point charge, Q, at a distance, r, is given by:
E = k * Q / r^2
where k is the Coulomb's constant (8.99 x 10^9 N m^2/C^2).
a) For -55.0 m:
We have a point charge Q1 = -2 μC at x = 0 and a point charge Q2 = +8 μC at x = -0.5 m. To find the electric field at -55.0 m, we need to consider the contributions from both charges:
E1 = k * Q1 / r1^2
E2 = k * Q2 / r2^2
where r1 = 55.0 m and r2 = 55.0 m + 0.5 m = 55.5 m
Substituting the values:
E1 = (8.99 x 10^9 N m^2/C^2) * (-2 x 10^-6 C) / (55.0 m)^2
E2 = (8.99 x 10^9 N m^2/C^2) * (8 x 10^-6 C) / (55.5 m)^2
Add the two contributions to get the total electric field:
E_total = E1 + E2
b) For -0.22 m:
The same procedure can be used to find the electric field at this point.
c) For 92 m:
Follow the same steps as above to find the electric field.
d) To find the point where the electric field is zero (apart from x = infinite), we need to consider the net contribution from charges Q1 and Q2. At this point, the electric field created by Q1 should be equal in magnitude but opposite in direction to the electric field created by Q2.
Write down the equations for electric field E1 and E2 and set them equal:
E1 = E2
k * Q1 / r1^2 = k * Q2 / r2^2
Solve for the distance r2 from Q2 to find the point where the electric field is zero.