Two point charges are 10.0 cm apart and have charges of 2.0 μC and –2.0 μC, respectively. What is the magnitude of the electric field at the midpoint between the two charges?
8.99*10^9(2*10^-6/.025)=719200
Two equal charges are separated by 3.7 x 10-10 m. The force between the charges has a magnitude of 2.37 x 10-3 N. What is the magnitude of q on the charges?
1.9x10^-16 (I got this using Coulomb's Law and working backward)
Thanks in advance!
Wait, can you please explain the first answer? What am I supposed to double? And after I double it, do I do what I did originally?
To find the magnitude of the electric field at the midpoint between two charges, you can use the formula for electric field:
E = k * (q1 / r1^2 + q2 / r2^2)
where:
E is the electric field,
k is the Coulomb's constant (8.99 x 10^9 N m^2 / C^2),
q1 and q2 are the charges,
r1 and r2 are the distances from the charges to the point where you want to calculate the electric field.
In the first question, the charges are 10.0 cm (or 0.1 m) apart. So, the distances from each charge to the midpoint are equal and equal to half the separation distance, which is 0.05 m or 5.0 cm.
Let's calculate the electric field at the midpoint:
E = (8.99 x 10^9 N m^2 / C^2) * ((2.0 x 10^-6 C) / (0.05 m)^2 + (-2.0 x 10^-6 C) / (0.05 m)^2)
Simplifying this expression, we get:
E = (8.99 x 10^9 N m^2 / C^2) * (2.0 x 10^-6 C - 2.0 x 10^-6 C) / (0.05 m)^2
E = (8.99 x 10^9 N m^2 / C^2) * 0 / (0.05 m)^2
E = 0
Therefore, the magnitude of the electric field at the midpoint between the two charges is 0.
Now, let's move on to the second question. To find the magnitude of the charge on the charges, we can use Coulomb's law:
F = k * (|q1 * q2| / r^2)
where:
F is the force,
k is the Coulomb's constant,
q1 and q2 are the charges,
r is the distance between the charges.
We can rearrange this equation to solve for the magnitude of q on the charges:
|q1 * q2| = F * r^2 / k
Plugging in the given values:
|q1 * q2| = (2.37 x 10^-3 N) * (3.7 x 10^-10 m)^2 / (8.99 x 10^9 N m^2 / C^2)
|q1 * q2| = 31.84 x 10^-26 C^2 / N
|q1 * q2| = 31.84 x 10^-26 C^2 / N
|q1 * q2| = 31.84 x 10^-26 C^2 / N
Since the charges are equal, we can assume q1 = q2 = q. So, we divide the magnitude by 2:
|q| = 31.84 x 10^-26 C^2 / (2 N)
|q| = 15.92 x 10^-26 C^2 / N
Thus, the magnitude of q on the charges is 15.92 x 10^-26 C.
Your first number is the E-field due to each charge. You have to double it, since they are both in the same direction.
For the second case,
8.99*10^9*q^2/(3.7*10^-10)^2 = 2.37*10^-3
q^2 = 3.61*10^032 C^2
q = 1.90*10^-16 C
I agree with your answer.