6. There are three charges (A, B, and C) at the corners of an equilateral triangle with sides of 5 cm. The charge of A is 2.5 × 10–7 C, B is –2.5 × 10–7 C, and C is 1.0 × 10–7 C. How much is the electrical force on the charge at C due to the other two charges?

Answer :

ANSWER:

0.09 N

STEP-BY-STEP EXPLANATION:

Given:

Charge A (qA) = 2.5 × 10^-7 C

Charge B (qB) = -2.5 × 10^-7 C

Charge C (qC) = 1 × 10^-7 C

Distance (d) = 5 cm = 0.05 m

The first thing is the electric force between AC and BC, using Coulom's law, just like this:

[tex]\begin{gathered} F_{12}=k\cdot\frac{q_1\cdot q_2}{d^2} \\ \\ \text{ We apply in each case:} \\ \\ F_{AC}=k\cdot\frac{q_A\cdot q_C}{d^2}=9\times10^9\cdot\frac{\left(2.5×10^{-7}\right)\left(1×10^{-7}\right)}{(0.05)^2}=0.09\text{ N} \\ \\ F_{BC}=k\cdot\frac{q_B\cdot q_C}{d^2}=9\times10^9\cdot\frac{(-2.5×10^{-7})(1×10^{-7})}{(0.05)^2}=-0.09\text{ N}=0.09\text{ N} \end{gathered}[/tex]

The resultant force due to the two forces is calculated using the following formula applied to the following angle, thus:

[tex]F=\sqrt{(F_{AC})^2+(F_{BC})^2+2\cdot F_{AC}\cdot F_{BC}\cdot\cos\theta}^[/tex]

We replace each value in order to calculate the electrical force on the charge at C due to the other two charges:

[tex]\begin{gathered} F=\sqrt{\left(0.09\right)^2+\left(0.09\right)^2+2\cdot0.09\cdot0.09\cdot\:\cos120°} \\ \\ F=\sqrt{0.0081+0.0081-0.0081} \\ \\ F=\sqrt{0.0081}=0.09\text{ N} \end{gathered}[/tex]

The electric force on the charge at C due to the other two charges is 0.09 N.

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