Two tiny particles having charges +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm. What are the magnitude and direction of electric field midway between these two charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²) A) 25.2 × $10^6$ N/C directed towards the negative charge B) 25.2 × $10^6$ N/C directed towards the positive charge C) 25.2 × $10^5$ N/C directed towards the negative charge D) 25.2 × $10^5$ N/C directed towards the positive charge E) 25.2 × $10^4$ N/C directed towards the negative charge

Question

Quizplus · Accepted Answer

To find the electric field midway between the two charges, we use the equation 
$$E=\frac{kq}{r^2}$$
where $k$ is the Coulomb's constant, $q$ is the charge and $r$ is the distance between the charges.

First, we need to find the distance from the midpoint to each of the charges. Half of the separation distance is 10.0 cm. Using Pythagoras theorem, the distance from the midpoint to the +20.0 μC is:
$$\sqrt{(20\,\text{cm})^2+(10\,\text{cm})^2}=22.4\,\text{cm}$$
and the distance to the -8.00 μC charge is also 22.4 cm.

Now we can calculate the electric field due to each charge at the midpoint, and then add them vectorially. The direction of the electric field due to the positive charge is away from it, and the direction due to the negative charge is towards it. Since the negative charge is closer to the midpoint, its electric field will be stronger, and its direction will dominate.

Thus, the electric field at the midpoint is:
$$E=\frac{kq_1}{r_1^2}+\frac{kq_2}{r_2^2}=\frac{(9.0\times10^9\,\text{N}\cdot\text{m}^2/\text{C}^2)(-8.00\times10^{-6}\,\text{C})}{(0.224\,\text{m})^2}+\frac{(9.0\times10^9\,\text{N}\cdot\text{m}^2/\text{C}^2)(20.0\times10^{-6}\,\text{C})}{(0.224\,\text{m})^2}=-2.13\times10^6\,\text{N/C}+7.07\times10^6\,\text{N/C}=4.94\times10^6\,\text{N/C}$$
directed towards the negative charge.

Therefore, the best choice is A, 25.2 × $10^6$ N/C directed towards the negative charge.

Two Tiny Particles Having Charges +20 10610^6106 N/C Directed Towards the Negative Charge B) 25

Two Tiny Particles Having Charges +20 $10^6$ N/C Directed Towards the Negative Charge
B) 25