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 outside [AB] such that :
a) AC=50cm b) AC=30cm c) AC=20cm d) point C does not exist
See prev post
To find the distance AC where the electric field is null, we need to use the principle that the electric field due to two point charges cancel each other out at certain points.
The electric field due to a point charge is given by the equation:
E = k * q / r^2
Where E is the electric field, k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance between the point charge and the point where we want to find the electric field.
In this case, we have two point charges q1 = -10^-5 C and q2 = -9×10^-5 C placed at points A and B, respectively, 40 cm apart.
Let's assume that point C is at a distance x from point A. Therefore, the distance from point C to point B would be (40 - x) cm.
We can now calculate the electric fields due to each point charge at point C:
E1 = k * q1 / (x^2)
E2 = k * q2 / ((40 - x)^2)
According to the problem, the electric field is null at point C. This means that the total electric field at point C is zero.
E_total = E1 + E2 = 0
Substituting the expressions for E1 and E2 into the equation above:
k * q1 / (x^2) + k * q2 / ((40 - x)^2) = 0
Now, let's solve this equation to find the value of x.