Two point charges are 2.00 m apart as shown on the right. The charge of the first object is -1.50 C, while the second object has a charge of +6.85 C. At which point will the electric field vector be zero?
in shortcut
To find the point at which the electric field vector is zero, we can use the principle of superposition. The electric field at a point due to both charges is the vector sum of the electric fields due to each charge separately.
Let's assume that the positive charge (+6.85 C) is located at point A, and the negative charge (-1.50 C) is located at point B. We want to find the point at which the electric field is zero.
Since the electric field due to a point charge is directed radially outward for a positive charge and radially inward for a negative charge, the electric field at point A due to the positive charge is directed away from point A and the electric field at point A due to the negative charge is directed towards point A.
At a point between A and B, the electric field at that point due to the positive charge will be stronger than the electric field due to the negative charge because the positive charge is bigger in magnitude. Therefore, the net electric field at that point will be directed away from point A.
At a point beyond B, the electric field at that point due to the negative charge will be stronger than the electric field due to the positive charge because the negative charge is closer to that point. Therefore, the net electric field at that point will be directed towards point A.
Therefore, if we move from point A towards point B, there must be a point where the electric field changes direction from away to towards point A. This is the point where the electric field is zero.
Therefore, the electric field vector will be zero at a point somewhere between the two charges, closer to the negative charge (-1.50 C).
Note: The specific location of the point at which the electric field is zero can be found by setting up an equation using Coulomb's law and solving for the distance from the negative charge (-1.50 C). However, no specific distances or coordinates are provided in the question, so we can only determine that the point will be between the two charges.
To find the point where the electric field vector is zero, we can use the principle of superposition. The electric field at a point is the vector sum of the electric fields created by each of the charges.
Given that the first object has a charge of -1.50 C and the second object has a charge of +6.85 C, and they are 2.00 m apart, we need to find the location where the electric fields created by these charges cancel each other out.
Let's assume that the point where the electric field is zero is at a distance x from the -1.50 C charge. Therefore, it is at a distance 2.00 m - x from the +6.85 C charge.
By Coulomb's law, the electric field created by a point charge q at a distance r is given by E = k*q/r^2, where k is the electrostatic constant.
For the -1.50 C charge at distance x, the electric field it creates is E1 = k*(-1.50 C) / (x^2).
For the +6.85 C charge at distance 2.00 m - x, the electric field it creates is E2 = k*(6.85 C) / ((2.00 m - x)^2).
For the electric field to be zero, E1 + E2 = 0.
So, we can solve the equation: k*(-1.50 C) / (x^2) + k*(6.85 C) / ((2.00 m - x)^2) = 0.
Simplifying the equation and solving for x will give us the location where the electric field is zero. Unfortunately, I cannot provide the numerical value or exact location since you did not provide the values for k and units for distance.
To find the point where the electric field vector is zero, we need to use the concept of electric field due to a point charge.
The electric field due to a point charge is given by the equation:
E = (k * q) / r^2
Where:
- E is the electric field
- k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2)
- q is the magnitude of the charge
- r is the distance from the charge to the point where the electric field is being calculated
Given that the first charge is -1.50 C and the second charge is +6.85 C, we can see that the electric fields due to these charges will be of opposite sign (negative and positive) since the charges have opposite signs.
To find the point where the electric field is zero, we need to set the electric fields due to these charges equal to each other and solve for the distance from the charges.
So, we can set up the equation:
(k * q1) / r1^2 = (k * q2) / r2^2
Where:
- q1 is the charge of the first object (-1.50 C)
- q2 is the charge of the second object (+6.85 C)
- r1 is the distance from the first object to the desired point where the electric field is zero
- r2 is the distance from the second object to the desired point where the electric field is zero
Plugging in the values:
(9 x 10^9 Nm^2/C^2 * -1.50 C) / r1^2 = (9 x 10^9 Nm^2/C^2 * 6.85 C) / r2^2
Simplifying the equation, we can cross-multiply and rearrange:
-1.50 / r1^2 = 6.85 / r2^2
Now, we know that the total distance between the charges is 2.00 m. So we can write:
r1 + r2 = 2.00 m
Now we have a system of equations. Solving this system will give us the values of r1 and r2, representing the distances from each charge to the desired point where the electric field is zero.