Three charges were positioned as shown in the figure below. If Q1=Q2=8uc
and d=0.5m, determine q if the electric field at is zero.
q=-11uc
u stands fr micro
Well, if the electric field at a certain point is zero, it means that the total electric field due to all the charges at that point cancels out. So let's see if we can find a combination of charges that does just that.
In this case, we have two positive charges, Q1 and Q2, so their electric fields point away from them. And we also have a negative charge, q, so its electric field points toward it.
To make the electric field at the given point zero, we need the electric fields of Q1 and Q2 to cancel out the electric field of q. Since the electric field is a vector quantity, this means the magnitudes of the electric fields need to be equal, and they should point in opposite directions.
So, let's see how we can achieve that. Since Q1 and Q2 have the same magnitude and are equidistant from the given point, their electric fields will have the same magnitude as well. Therefore, we need to make the magnitude of q's electric field equal to that of Q1 and Q2.
Using the formula for the electric field due to a point charge, E = k * q / r^2, where k is the Coulomb's constant, q is the charge, and r is the distance, we can set up an equation:
k * q / (0.5^2) = k * 8uC / (d^2)
Simplifying, we have:
q = (d^2 * 8uC) / 0.5^2
q = (0.5^2 * 8uC) / 0.5^2
q = 8uC
Therefore, if the electric field at the given point is zero, q should be equal to 8uC.
Just remember, this is an approximate calculation based on the given information. The actual result can vary depending on the precise positions and magnitudes of the charges.
To determine the value of q when the electric field at the point P is zero, we need to analyze the electric field contributions from each charge at that point.
Let's consider charge Q1 located at point A. The electric field created by Q1 at point P can be calculated using Coulomb's Law:
E1 = k * (Q1 / r1^2)
Here, k is the electrostatic constant (k = 9 * 10^9 Nm^2/C^2), Q1 is the magnitude of charge Q1 (Q1 = 8 μC = 8 * 10^-6 C), and r1 is the distance between Q1 and P (r1 = 0.5 m).
Now, let's consider charge Q2 located at point B. The electric field created by Q2 at point P can also be calculated using Coulomb's Law:
E2 = k * (Q2 / r2^2)
In this case, Q2 has the same magnitude as Q1 (Q2 = 8 μC = 8 * 10^-6 C), and r2 is also 0.5 m since point B is located at the same distance from point P.
Next, let's consider charge q located at point C. The electric field created by q at point P can be calculated as:
E3 = k * (q / r3^2)
Here, r3 is the distance between q and P. We need to determine the value of q when the electric field at point P is zero.
Now, observe that if the electric field at point P is zero, the contribution of E1 and E2 (due to charges Q1 and Q2) at point P must cancel out the contribution from E3 (due to charge q).
Since E1 and E2 have equal magnitudes and are directed towards opposite directions (because of the equal magnitude and opposite charge of Q1 and Q2), the net electric field due to Q1 and Q2 at point P will be zero if they have the same magnitudes as E3.
Therefore, we conclude that:
E1 + E2 = E3
Substituting the formulas for E1, E2, and E3:
k * (Q1 / r1^2) + k * (Q2 / r2^2) = k * (q / r3^2)
Simplifying:
Q1 / r1^2 + Q2 / r2^2 = q / r3^2
Plugging the known values:
(8 * 10^-6 C) / (0.5 m)^2 + (8 * 10^-6 C) / (0.5 m)^2 = q / (r3)^2
(8 * 10^-6 C) / (0.25 m^2) + (8 * 10^-6 C) / (0.25 m^2) = q / (r3)^2
Solving this equation will give us the value of q when the electric field at point P is zero.