Two charges are placed on the x axis. One of the charges (q1 = +6.14C) is at x1 = +3.00 cm and the other (q2 = -28.6C) is at x2 = +9.00 cm. Find the net electric field (magnitude and direction given as a plus or minus sign) at (a) x = 0 cm and (b) x = +6.00 cm.
At x = 0, charge q1 creates an electric field in the -x direction and charge q2 creates an electric field in the +x direction. Use the Coulomb equation
E = kq/r^2
for the E fields and add them, taking the sign into account.
At x = 6.00 cm, you are between q1 and q2, and the E fields due to the two charges are in the same direction (+x).
To find the net electric field at a specific point, we need to calculate the electric field produced by each charge and then sum them up.
The electric field produced by a point charge is given by Coulomb's law:
E = k * (q / r^2)
where E is the electric field, k is the Coulomb's constant (8.99 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.
Let's find the net electric field at (a) x = 0 cm:
First, calculate the electric field produced by q1 at x = 0 cm:
r1 = 0.03 m - 0 m = 0.03 m
E1 = k * (q1 / r1^2)
Next, calculate the electric field produced by q2 at x = 0 cm:
r2 = 0.09 m - 0 m = 0.09 m
E2 = k * (q2 / r2^2)
Notice that q2 is negative, which means it will create an electric field in the opposite direction.
To find the net electric field, add the individual electric fields together:
E_net_a = E1 + E2
Now let's find the net electric field at (b) x = +6.00 cm:
First, calculate the electric field produced by q1 at x = +6.00 cm:
r1 = 0.03 m - 0.06 m = 0.03 m
E1 = k * (q1 / r1^2)
Next, calculate the electric field produced by q2 at x = +6.00 cm:
r2 = 0.09 m - 0.06 m = 0.03 m
E2 = k * (q2 / r2^2)
Again, q2 is negative, so the electric field will be in the opposite direction.
To find the net electric field, add the individual electric fields together:
E_net_b = E1 + E2
Finally, we have obtained the net electric field at points (a) and (b). To determine the magnitude and direction, substitute the calculated values into the equations and provide the appropriate sign.