Where between two charges is the electric field zero?
2 Answers
To find the point between two charges where the electric field is zero, you can use the principle of superposition.
Assume you have two point charges: \( q_1 \) and \( q_2 \). The electric field \( E \) due to a point charge is given by:
\[
E = k \frac{|q|}{r^2}
\]
where \( k \) is Coulomb's constant, \( q \) is the charge, and \( r \) is the distance from the charge.
### Steps to find the zero electric field point:
1. **Identify the charges**: Assume \( q_1 \) is positive and \( q_2 \) is negative (or vice versa).
2. **Determine the region**: The point where the electric field is zero will be along the line connecting the two charges. You should look for a point between them, but it could also be outside, depending on the magnitudes and signs of the charges.
3. **Set up the equation**: If the charges are \( q_1 \) and \( q_2 \) separated by a distance \( d \), let \( x \) be the distance from \( q_1 \) to the point where the electric field is zero. The distance from \( q_2 \) to that point would then be \( d - x \).
4. **Write the electric fields**: The electric fields due to each charge at that point will be:
- Due to \( q_1 \): \( E_1 = k \frac{|q_1|}{x^2} \)
- Due to \( q_2 \): \( E_2 = k \frac{|q_2|}{(d - x)^2} \)
5. **Set them equal**: For the electric field to be zero, the magnitudes must be equal:
\[
k \frac{|q_1|}{x^2} = k \frac{|q_2|}{(d - x)^2}
\]
Simplifying this gives:
\[
\frac{|q_1|}{x^2} = \frac{|q_2|}{(d - x)^2}
\]
6. **Cross-multiply and solve for \( x \)**:
\[
|q_1| (d - x)^2 = |q_2| x^2
\]
Expanding and rearranging will lead to a quadratic equation in \( x \).
7. **Evaluate possible solutions**: Depending on the relative magnitudes of the charges, you may find that the zero field point lies either between the charges or outside of them.
### Conclusion
To determine the specific location, you will need the values of \( q_1 \) and \( q_2 \). If they are of opposite signs, there will definitely be a point between them where the field is zero. If they are both positive or both negative, there won't be a point between them; instead, look outside.
Assume you have two point charges: \( q_1 \) and \( q_2 \). The electric field \( E \) due to a point charge is given by:
\[
E = k \frac{|q|}{r^2}
\]
where \( k \) is Coulomb's constant, \( q \) is the charge, and \( r \) is the distance from the charge.
### Steps to find the zero electric field point:
1. **Identify the charges**: Assume \( q_1 \) is positive and \( q_2 \) is negative (or vice versa).
2. **Determine the region**: The point where the electric field is zero will be along the line connecting the two charges. You should look for a point between them, but it could also be outside, depending on the magnitudes and signs of the charges.
3. **Set up the equation**: If the charges are \( q_1 \) and \( q_2 \) separated by a distance \( d \), let \( x \) be the distance from \( q_1 \) to the point where the electric field is zero. The distance from \( q_2 \) to that point would then be \( d - x \).
4. **Write the electric fields**: The electric fields due to each charge at that point will be:
- Due to \( q_1 \): \( E_1 = k \frac{|q_1|}{x^2} \)
- Due to \( q_2 \): \( E_2 = k \frac{|q_2|}{(d - x)^2} \)
5. **Set them equal**: For the electric field to be zero, the magnitudes must be equal:
\[
k \frac{|q_1|}{x^2} = k \frac{|q_2|}{(d - x)^2}
\]
Simplifying this gives:
\[
\frac{|q_1|}{x^2} = \frac{|q_2|}{(d - x)^2}
\]
6. **Cross-multiply and solve for \( x \)**:
\[
|q_1| (d - x)^2 = |q_2| x^2
\]
Expanding and rearranging will lead to a quadratic equation in \( x \).
7. **Evaluate possible solutions**: Depending on the relative magnitudes of the charges, you may find that the zero field point lies either between the charges or outside of them.
### Conclusion
To determine the specific location, you will need the values of \( q_1 \) and \( q_2 \). If they are of opposite signs, there will definitely be a point between them where the field is zero. If they are both positive or both negative, there won't be a point between them; instead, look outside.
To determine where the electric field between two charges is zero, you need to know the magnitudes and signs of the charges. If you have two charges, \( q_1 \) and \( q_2 \), and they are separated by a distance \( d \), the point where the electric field is zero is found by setting up the condition where the magnitudes of the electric fields due to each charge at that point are equal and opposite.
Assuming \( q_1 \) and \( q_2 \) are of opposite signs, the electric field will be zero at a point along the line connecting the two charges. To find this point:
1. **Set up the equation for electric fields**: Let \( x \) be the distance from \( q_1 \) where the electric field is zero. The distance from \( q_2 \) to this point will be \( d - x \).
2. **Apply the formula for electric fields**: The electric field \( E \) due to a charge \( q \) at a distance \( r \) is given by \( E = \frac{k|q|}{r^2} \), where \( k \) is Coulomb’s constant.
3. **Set the fields equal**: For zero net electric field, the magnitudes of the electric fields must be equal:
\[
\frac{k|q_1|}{x^2} = \frac{k|q_2|}{(d - x)^2}
\]
4. **Solve for \( x \)**: Rearranging the equation and solving for \( x \) gives you the distance from \( q_1 \) where the electric field is zero.
If the charges have the same sign, there will be no point between them where the electric field is zero.
Assuming \( q_1 \) and \( q_2 \) are of opposite signs, the electric field will be zero at a point along the line connecting the two charges. To find this point:
1. **Set up the equation for electric fields**: Let \( x \) be the distance from \( q_1 \) where the electric field is zero. The distance from \( q_2 \) to this point will be \( d - x \).
2. **Apply the formula for electric fields**: The electric field \( E \) due to a charge \( q \) at a distance \( r \) is given by \( E = \frac{k|q|}{r^2} \), where \( k \) is Coulomb’s constant.
3. **Set the fields equal**: For zero net electric field, the magnitudes of the electric fields must be equal:
\[
\frac{k|q_1|}{x^2} = \frac{k|q_2|}{(d - x)^2}
\]
4. **Solve for \( x \)**: Rearranging the equation and solving for \( x \) gives you the distance from \( q_1 \) where the electric field is zero.
If the charges have the same sign, there will be no point between them where the electric field is zero.