Multiple choice (show your work if any):
1) Two point charges q1=-10^-5 C and q2=-9×10^-5 C are placed respectively at two points A and B 40 cm apart. The electric field is null at a point C of [AB] such that :
a) AC=50cm b) AC=10cm c) AC=20cm d) point C doesn't exist
2) Same given. The electric field is null at a point C outside [AB] such that :
a) AC=50cm b) AC=30cm c) AC=20cm d) point C does not exist
E1 = kq1/r^2
same for E2
where do vectors cancel?
To determine the answer for each question, we need to consider the concept of electric fields. The electric field at a point in space is the force experienced by a positive test charge placed at that point.
1) For the first question, we have two point charges q1 and q2 placed at points A and B, respectively. The electric field is null (zero) at a point C along the line segment AB. We want to find the distance AC.
To solve this, we can use the principle of superposition. The net electric field at any point due to multiple charges is the vector sum of the electric fields produced by each individual charge. The net electric field at point C due to q1 and q2 must be zero.
Mathematically, we can write:
E_total = E_q1 + E_q2 = 0
The electric field due to a point charge q at a distance r from the charge is given by the equation:
E = k * q / r^2
where k is the electrostatic constant (9 * 10^9 Nm^2/C^2).
Applying this equation to both charges at point C, we get:
E_q1 = k * q1 / (AC)^2
E_q2 = k * q2 / (BC)^2
Since the electric field at C is null, we have:
E_total = E_q1 + E_q2 = 0
Substituting the values:
k * q1 / (AC)^2 + k * q2 / (BC)^2 = 0
We are given the values of q1, q2, and the distance between A and B (40 cm). We need to solve for AC.
This is a straightforward algebraic equation where the unknown is AC. Solving the equation will give us the distance AC.
2) For the second question, we are asked to find the distance AC outside the line segment AB, where the electric field is null.
We can follow a similar approach as in the first question. Using the principle of superposition, we set the net electric field at point C due to q1 and q2 equal to zero:
E_total = E_q1 + E_q2 = 0
Substituting the equation for electric fields, we have:
k * q1 / (AC)^2 + k * q2 / (CB)^2 = 0
Again, we are given the values of q1, q2, and the distance between A and B (40 cm). We need to solve for AC.
By solving the above equation, we can find the distance AC outside the line segment AB where the electric field is null.
So, to determine the correct answer for each question, you will need to solve the respective algebraic equations using the given information about charges and distances.