A doorframe is twice as tall as it is wide. There is a positive charge on the top left corner and an equal but negative charge in the top right corner. What is the direction of the electric force due to these charges on a negatively charged dust mite in the bottom left corner of the doorframe?

α = 141.5°  (counterclockwise)

Explanation:

If

q₁ = +q

q₂ = -q

q₃ < 0

b = 2*a

We apply Coulomb's Law as follows

F₁₃ = K*q₁*q₃ / d₁₃² = + K*q*q₃ / (2*a)² = + K*q*q₃ / (4*a²)

F₂₃ = K*q₂*q₃ / d₂₃² = - K*q*q₃ / (5*a²)

(d₂₃² = a² + (2a)² = 5*a²)

Then

∅ = tan⁻¹(2a/a) = tan⁻¹(2) = 63.435°

we apply

F₃x = - F₂₃*Cos ∅ = - (K*q*q₃ / (5*a²))* Cos 63.435°

⇒  F₃x = - 0.0894*K*q*q₃ / a²

F₃y = - F₂₃*Sin ∅ + F₁₃

⇒  F₃y = - (K*q*q₃ / (5*a²))* Sin 63.435° + (K*q*q₃ / (4*a²))

⇒  F₃y = 0.0711*K*q*q₃ / a²

Now, we use the formula

α = tan⁻¹(F₃y / F₃x)

⇒  α = tan⁻¹((0.0711*K*q*q₃ / a²) / (- 0.0894*K*q*q₃ / a²)) = - 38.5°

The real angle is

α = 180° - 38.5° = 141.5°  (counterclockwise)

when a device is used in a circuit in which the voltage is 81 v, the current flowing through the device is 3 a. what is the resistance of the device?

a. 27 ω

b. 40.5 a

c. 243 ω

d. 243 a

the correct answer is a. 27

the chart show the masses and velocities of two colliding objects that stick together after a collision.

according to the law of conservation of momentum, the momentum of the object after the collision is  

answer

1,500

kg • m/s.