A positive charge of 5.0×10^−5 C is 0.040 m from a second positive charge of 2.0×10^−6 C. Calculate the force between the charges.

Question

Responses

5.6×10^−2 N

5.6x10^2 N
1.4×10^−2 N

2.3×10^1 N

Answer 1

To calculate the force between two charges, we can use Coulomb's Law, which is given by the formula:

$$F=k\frac{|q_1{q}_2|}{r^2}$$

where:

• $F$ is the force between the charges,
• $k$ is Coulomb's constant $(8.99\times {10}^9,{\text{N m}}^2/{\text{C}}^2)$,
• $q_1$ and $q_2$ are the magnitudes of the charges,
• $r$ is the distance between the charges.

Given:

• $q_1=5.0\times {10}^{-5},C$
• $q_2=2.0\times {10}^{-6},C$
• $r=0.040,m$

Substituting these values into the formula:

$$F=(8.99\times {10}^9)\frac{(5.0\times {10}^{-5})(2.0\times {10}^{-6})}{(0.040{)}^2}$$

Calculating $(0.040{)}^2$:

$$(0.040{)}^2=0.0016,m^2$$

Now substituting this back into the equation for force:

$$F=(8.99\times {10}^9)\frac{(5.0\times {10}^{-5})(2.0\times {10}^{-6})}{0.0016}$$

Calculating the product of the charges:

$$(5.0\times {10}^{-5})(2.0\times {10}^{-6})=1.0\times {10}^{-10}$$

Now substituting:

$$F=(8.99\times {10}^9)\frac{1.0\times {10}^{-10}}{0.0016}$$

This simplifies to:

$$F=(8.99\times {10}^9)\frac{1.0\times {10}^{-10}}{1.6\times {10}^{-3}}$$

Calculating $\frac{1.0\times {10}^{-10}}{1.6\times {10}^{-3}}$:

$$\frac{1.0\times {10}^{-10}}{1.6\times {10}^{-3}}=0.625\times {10}^{-7}=6.25\times {10}^{-8}$$

Now calculating the force:

$$F=(8.99\times {10}^9)(6.25\times {10}^{-8})$$

Calculating this product:

$$F=8.99\times 6.25\times {10}^{9-8}=56.1875,N\approx 5.6\times {10}^{1}N$$

Thus, the force between the charges is approximately 5.6 × 10^1 N.