A particle with charge 2-µC is placed at the origin, an identical particle, with the same charge,
is placed 2m from the origin on the x axis, and a third identical particle, with the same charge,
is placed 2m from the origin on the y axis. The magnitude of the force on the particle at the
origin is:
A. 9.0 × 10-3 N
B. 6.4 × 10-3 N
C. 1.3 × 10-2 N
D. 1.8 × 10-2 N
E. 3.6 × 10-2 N

1.3 × 10-2 N

Explanation:

Coulomb's law relate the force between two charges as

F = kq₁q₂ / d² where q₁ is at the origin

q₁ = q₂ = q₃= 2 µC = 2 × 10⁻⁶ C

F₁₂ = 8.99 × 10⁹ × 2 × 10⁻⁶ × 2 × 10⁻⁶ / 4 = 0.009 N along x axis

F₁₃ along y axis = 8.99 × 10⁹× 2 × 10⁻⁶ × 2 × 10⁻⁶ / 4 = 0.009 N along y axis

the magnitude of the force on the particle at the origin = √ (0.009² + 0.009²) = 1.27 × 10 ⁻² N approx 1.3 × 10-2 N

you would expect a sound wave to speed up. - b)

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: