Three point charges are arranged as shown.
− + +
−6.1 nC and 1.6 nC .4m apart
1.6 nC and 3 nC .088m apart
What is the electric field strength
at 1.8 m to the right of the mid
The point where we have to find the electric field is separated by r1 = 3.844 m from the first charge, by r2 = 0.156 m from the second charge, and by r3 =0.244 m from the third charge.
E1, E2 and E3 are directed to the left.
The net electric field is
E =E1 +E2 +E3 = k•|q1| /(r1)^2 + k•q2 /(r2)^2 + k•q3 /(r3)^2,
where k =9•10^9 N•m^2•m^-2.
To find the electric field strength at a point, we need to calculate the individual electric fields generated by each point charge and then add them together. The electric field due to a point charge is given by the equation:
E = k * Q / r^2
where E is the electric field strength, k is Coulomb's constant (k = 9 x 10^9 Nm^2/C^2), Q is the charge of the point charge, and r is the distance between the point charge and the point where we want to calculate the electric field.
Let's calculate the electric field due to each point charge separately:
For the -6.1 nC charge (let's call it Charge A), we have:
Q = -6.1 nC
r = 1.8 m (since the point we want to calculate the electric field at is 1.8 m to the right of the mid)
Using the equation for electric field, we have:
E_A = k * Q / r^2
Plugging in the values:
E_A = (9 x 10^9 Nm^2/C^2) * (-6.1 x 10^-9 C) / (1.8 m)^2
Now, calculate the electric field due to the other point charges using the same approach.
For the 1.6 nC charge (let's call it Charge B), we have:
Q = 1.6 nC
r = 0.088 m (distance between Charge B and the midpoint)
E_B = k * Q / r^2
And for the 3 nC charge (let's call it Charge C), we have:
Q = 3 nC
r = 0.088 m (distance between Charge C and the midpoint)
E_C = k * Q / r^2
Now, add up the individual electric fields to get the total electric field at the point 1.8 m to the right of the midpoint:
E_total = E_A + E_B + E_C
Calculate the values of E_A, E_B, and E_C using the equations provided, and then add them together to get the total electric field at the desired point.