In many practical applications, we use variable electric current I(t), that is, the current that changes with time t. A couple of examples that we will consider in this problem: (a) Current I(t)=I0 cos(2πf·t) that oscillates with frequency f. (b) Current I(t)=I0 e−t/ that decays in time with time constant . Our questions will be related to the currents with amplitude I0=1.56 A running in the copper (resistivity = 1.7 10-8 Ω·m) wire of diameter d=3 mm and length l=0.56 m. For example (a), how much energy Wa is dissipated in the wire via Joule heating during one period of current oscillations for frequency f=50.4 Hz?: Wa= mJ. With the oscillating current, the amount of charge passing through any cross-section of the wire would, of course, also oscillate with the same frequency. What is the amplitude Q0 of charge oscillations?:

Answer: a charge of -1.0  × 10⁻⁴ c must be placed  at x = 26 m.the sign of the charge will be the same sign as the  -4.0  µc charge.======electricstatic force between two point charges  is given by    where k is coulomb's constant,  8.99×10⁹  n·m²/c², q₁ and q₂ are the point charges, and r is the distance between the two point charges.assign positive to q₁let q₁ =  6.0 µc, q₂ = -4.0  µc, q₀ represent the charge at the origin, and q₃ represent this new charge to place.the charge at the origin q₀ would experience the following force f₀₁ from q₁, with r = 6.0 m (note that 1  µc = 10⁻⁶ c)    the force from q₂    the force from q₃    the net force on the origin charge, q₀, has to be zero for no electrostatic forcehaving an equation where k and q₀ can be divided out of the equation will allow us to solve for q₃    isolating:     a charge of -1.0  × 10⁻⁴ c must be placed  at x = 26 m.the sign of the charge will be the same as the  -4.0  µc charge