Where is the electric field zero?

In summary, two point charges are placed 1.00m apart. The electric field is zero at infinity, but between q(1) and q(2) the electric fields are both negative.
  • #1
CatWhisperer
40
1

Homework Statement



Two point charges are placed 1.00m apart.
q(1) = -2.50 x 10^(-6) C
q(2) = +6.00 x 10^(-6) C
Task is to find where along the line, other than at infinity, the electric field will be equal to zero.

Homework Equations



E = (k * q) / r^2

The Attempt at a Solution



I let E(1) + E(2) = 0 and substituted the above formula in, which, after simplifying gives me a quadratic (I let 'x' equal the first radius, and '1.00 - x' equal the second, so q(1) is at zero on the axis, and the solution for x will give me the point on the axis with respect to q1 at which the two fields cancel out and the net field equals zero).

I solved the quadratic and came up with:

x = 0.39m (0.39m to the right of q(1) ) and
x = -1.83m (1.83m to the left of q (1) )

The answer is -1.83m, but I am wondering if someone can explain why +0.39m isn't correct also? I think my conceptual understanding is lacking here, and my textbook hasn't quite revealed the answer.

Thanks very much in advance, folks.
 
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  • #2
CatWhisperer said:

Homework Statement



Two point charges are placed 1.00m apart.
q(1) = -2.50 x 10^(-6) C
q(2) = +6.00 x 10^(-6) C
Task is to find where along the line, other than at infinity, the electric field will be equal to zero.

Homework Equations



E = (k * q) / r^2

The Attempt at a Solution



I let E(1) + E(2) = 0 and substituted the above formula in, which, after simplifying gives me a quadratic (I let 'x' equal the first radius, and '1.00 - x' equal the second, so q(1) is at zero on the axis, and the solution for x will give me the point on the axis with respect to q1 at which the two fields cancel out and the net field equals zero).

I solved the quadratic and came up with:

x = 0.39m (0.39m to the right of q(1) ) and
x = -1.83m (1.83m to the left of q (1) )

The answer is -1.83m, but I am wondering if someone can explain why +0.39m isn't correct also? I think my conceptual understanding is lacking here, and my textbook hasn't quite revealed the answer.

Thanks very much in advance, folks.
What specifically are you using for E(1) & E(2) ?
 
  • #3
I have substituted the formula E = k(e) * q / r^2

So I get:

E(net) = E(1) + E(2)

Where

E(1) = k(e) * q(1) / r(1)^2
E(2) = k(e) * q(2) / r(2)^2

k(e) = 8.99 * 10^9
r(1) = x
r(2) = 1.00 - x
q(1) & q(2) as given in the OP
 
  • #4
CatWhisperer said:
I have substituted the formula E = k(e) * q / r^2

So I get:

E(net) = E(1) + E(2)

Where

E(1) = k(e) * q(1) / r(1)^2
E(2) = k(e) * q(2) / r(2)^2

k(e) = 8.99 * 10^9
r(1) = x
r(2) = 1.00 - x
q(1) & q(2) as given in the OP
So, you have q(1) at the origin, and q(2) on the x-axis at x = 1 meter.

You also have E(1) being negative and E(2) being positive, (but all the algebra "cares about" is that they have opposite sign). Those signs will be that way only to the right of q(2). They wil both be opposite that to the left of q(1) so the results will still be good there.

Between q(1) and q(2), both E(1) and E(2) point to the left, i.e., they're both negative.
 
  • #5
Gotcha. The fields can't cancel out unless they point in opposite directions, which happens on the left of q1 (and the right of q2, but then other conditions are not met), but not between q1 and q2 :-)

Thank you!
 

1. What is the concept of the electric field?

The electric field is a physical quantity that describes the force exerted on a charged particle by other charged particles in its vicinity. It is a vector quantity, meaning it has both magnitude and direction.

2. Why does the electric field become zero?

The electric field becomes zero when there is a balance between the positive and negative charges in a given space. This can happen in various scenarios, such as when two equal and opposite charges cancel each other out or when there is an equal distribution of charges in a conductor.

3. What are the factors that affect the electric field becoming zero?

The electric field becoming zero depends on the distribution of charges, the distance between the charges, and the medium in which the charges are located. Changing any of these factors can affect the electric field and cause it to become non-zero.

4. How can we calculate the point where the electric field is zero?

To calculate the point where the electric field is zero, we can use the principle of superposition to determine the net electric field at a specific point by adding up the contributions from individual charges. If the net electric field is zero, then the point is where the electric field is zero.

5. Why is it important to know where the electric field is zero?

Knowing where the electric field is zero is crucial in understanding the behavior of charged particles and predicting their movements. It also helps in designing and optimizing electrical systems, such as circuits and motors, to ensure that they function properly and efficiently.

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