There is a charge that is 1uC and another charge that is 2 uC. They are 10 cm apart. I need to find a point where the electric field is zero.
All I have is this kq1\a=kq2\(10-a)^2
where q1=1
where q2=2
where k=9*10^9
I am lost after this I know I use regular algebra but i don't get the right answer. Please help
The location where the field is zero is on a line between the two points where q1/d1^2 equals q2/d2^2
d1 + d2 = 10
Solve 1/d1^2 = 2/(10 - d1)^2)
d1 is the distance from charge 1 (1 uC)
So are you saying that for d1 I just put 10 or is that a variable
Alguém traduza isso,por favor ... =)
Duas cargas fixas de 1 e -3 (µC) estão separadas por uma distância de 10 cm?
Onde você deverá colocar uma terceira carga, para que nenhuma força atue sobre ela? Importa qual o sinal dessa carga?
To find the point where the electric field is zero, we can set the equation kq1/(a^2) = kq2/((10-a)^2) equal to zero.
Substituting the given values, we have:
(9 * 10^9 * 1) / (a^2) = (9 * 10^9 * 2) / ((10 - a)^2)
Now, let's simplify this equation step by step:
1. Cross multiply:
(9 * 10^9 * 1) * ((10 - a)^2) = (9 * 10^9 * 2) * (a^2)
2. Expand both sides of the equation:
(9 * 10^9) * ((10 - a) * (10 - a)) = (9 * 10^9 * 2) * (a * a)
3. Simplify both sides:
(9 * 10^9) * (100 - 20a + a^2) = (9 * 10^9 * 2) * a^2
4. Distribute the factor (9 * 10^9) on the left side:
900 - 180a + 9a^2 = 18a^2
5. Rearrange the equation by moving all terms to one side:
18a^2 - 9a^2 + 180a - 900 = 0
6. Combine like terms:
9a^2 + 180a - 900 = 0
Now we have a quadratic equation. To solve it, we can either factor or use the quadratic formula. Let's use the quadratic formula:
a = [-b ± sqrt(b^2 - 4ac)] / 2a
In our case, the equation is in the form:
9a^2 + 180a - 900 = 0
So, our coefficients are:
a = 9, b = 180, c = -900
Now let's substitute these values into the quadratic formula:
a = [-180 ± sqrt(180^2 - 4 * 9 * -900)] / (2 * 9)
Simplifying this further will give you two possible values for 'a'. These values represent the positions at which the electric field is zero.
d1 is a variable.
Solve the last equation I wrote to determine its value.
I did not say that d1 = 10