To find the point where a +2.0 C point charge feels no electric force, we need to consider the electric field vectors from the red and yellow charges separately and find the point where the vectors cancel out.
As the yellow charge is positive (+1.2 C), it creates an electric field that points away from it radially. On the other hand, the red charge is negative (-1.0 C), and its electric field vectors point towards it radially.
At any point along the line connecting the red and yellow charges, the electric fields due to each charge will have the same magnitude but opposite direction. Therefore, if we place the +2.0 C point charge on this line, the electric fields from the red and yellow charges will cancel each other out.
Let's calculate the distance from the red charge to the point where the yellow charge is located.
The distance between the red charge and the point between the charges is 1 m.
Now, consider the direction of the electric fields: since both the red and yellow charges are on the x-axis, the electric fields will only have an x-component.
Due to the symmetry, the electric fields will be equal in magnitude, so we need to find the distance on the x-axis where the electric field from the yellow charge cancels out the electric field from the red charge.
Using Coulomb's law to calculate the electric field:
Electric field from the red charge:
E_red = k * |q_red| / r_red^2
Electric field from the yellow charge:
E_yellow = k * |q_yellow| / r_yellow^2
The magnitudes of the electric fields are the same, so:
k * |q_red| / r_red^2 = k * |q_yellow| / r_yellow^2
Substituting the given values:
k * 1 C / r_red^2 = k * 1.2 C / (1 m - r_red)^2
Cross-multiplying:
r_red^2 = 1.2 * (1 m - r_red)^2
Expanding the square on the right side:
r_red^2 = 1.2 * (1 m - 2 * r_red + r_red^2)
Simplifying and rearranging the equation:
r_red^2 - 2.4 * r_red + 1.2 = 0
Using the quadratic formula (a = 1, b = -2.4, c = 1.2):
r_red = (-b ± √(b^2 - 4ac)) / (2a)
r_red = (-(-2.4) ± √((-2.4)^2 - 4 * 1 * 1.2)) / (2 * 1)
r_red = (2.4 ± √(5.76 - 4.8)) / 2
r_red = (2.4 ± √0.96) / 2
r_red = (2.4 ± 0.9798) / 2
The two possible values for r_red are:
r_red = (2.4 + 0.9798) / 2 = 1.6899 m or r_red = (2.4 - 0.9798) / 2 = 0.7101 m
Therefore, the +2.0 C point charge can be placed at a distance of 1.6899 m or 0.7101 m from the red charge along the x-axis, between the red and yellow charges, to feel no electric force.
Where could I put a point charge Q = +2.0 C such that it feels no electric force?
Red Charge: -1.0 C at (0 m, 0 m)
Yellow Charge: +1.2 C at (1 m, 0 m)
1 answer