Two point charges lie along the y-axis. A charge of q1 = -7 μC is at y = 6.0 m, and a charge of q2 = -6.5 μC is at y = -4.0 m. Locate the point (other than infinity) at which the total electric field is zero.
I have no clue where to start so any information will be greatly appreciated!
To locate the point where the total electric field is zero, we can use the principle of superposition, which states that the total electric field at a point due to multiple charges is the vector sum of the electric fields produced by each individual charge.
In this case, we have two point charges along the y-axis: q1 = -7 μC at y = 6.0 m and q2 = -6.5 μC at y = -4.0 m.
The electric field produced by a point charge can be calculated using Coulomb's law:
E = k * (|q| / r^2) * r-hat
Where:
- E is the electric field
- k is the electrostatic constant (k = 9 x 10^9 N*m^2/C^2)
- q is the charge magnitude
- r is the distance from the charge to the point where we want to calculate the electric field
- r-hat is the unit vector pointing from the charge to the point
To find the point where the total electric field is zero, we need to find a point where the electric field due to q1 cancels out the electric field due to q2.
Steps to find the point:
1. Assign variables for the distances and charges:
- q1 = -7 μC (at y1 = 6.0 m)
- q2 = -6.5 μC (at y2 = -4.0 m)
2. Set up expressions for the electric field due to each charge:
- E1 = k * (|q1| / r1^2)
- E2 = k * (|q2| / r2^2)
3. Substitute the expressions for electric field and distances:
- E1 = k * (|q1| / (y - y1)^2)
- E2 = k * (|q2| / (y - y2)^2)
4. Set up the equation that the total electric field is zero:
- E_total = E1 + E2 = 0
5. Solve the equation for the unknown variable y. This can be done algebraically or graphically.
6. Once you have found the value of y, you can substitute it back into the equation to find the corresponding x-coordinate if needed.
Note: It is essential to keep the signs of the charges and the direction of the electric fields in mind while calculating and considering the vector sum.
Following these steps, you can determine the point (other than infinity) at which the total electric field is zero.
Well, negative charges on either side of the x axis. So the E is in opposite directions between the charges, a likely place to find where they cancel (add to zero).
so set them equal
E1=E2 (they are in opposite directions)
k7e-6/(x+4)^2=k6.5e-6/(6-x)^2 this assumes x is on the right hand side. with that assumption, x should be positive.
7(6-x)^2=6.5(x+4)^2
take sqrt root of each side.
6-x=(x+4)sqrt(6.5/7)
let that last term be c
6-x-cx=4c
x(1+c)=6+4c
x= you do it. x is the position on the positive x side.
check my work.