A96-mh solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diameter. a coil is tightly wound around the solenoid at its center. the coil's resistance is 9.9 ohms. the mutual inductance of the coil and solenoid is 31 μh. at a given instant, the current in the solenoid is 540 ma, and is decreasing at the rate of 2.5 a/s. at the given instant, what is the magnitude of the induced current in the coil? (μ0 = 4π × 10-7 t ∙ m/a)

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