A very long, straight solenoid with a cross-sectional area of 1.94 cm^2 is wound with 87.2 turns of wire per centimeter. Starting at t = 0, the current in the solenoid is increasing according to i(t)=(0.160A/s^2)t^2. A secondary winding of 5.0 turns encircles the solenoid at its center, such that the secondary winding has the same cross-sectional area as the solenoid.
A) What is the magnitude of the emf induced in the secondary winding at the instant that the current in the solenoid is 3.2A ?

Given Information:  

current = I = 3.2 A

Area of solenoid = A = 1.94 cm² = 0.94x10⁻³ m²

Turns per cm at primary side = n = 87.2 turns/cm = 8720 turns/m

current at time 0 = i(t) = (0.160 A/s²) t²

Number of turns secondary side = N = 5 turns

Required Information:  

Induced emf at secondary side = ξ = ?  

Induced emf at secondary side ξ = -7.605x10⁻⁶ V

Explanation:

From the Faraday's law the induced EMF ξ is given by  

ξ = -NΔΦ/Δt  

t can be found using the given i(t)

3.2 = 0.160 t²

t² = 3.2/0.160

t = √3.2/0.160

t = 4.472 seconds

change in flux ΔΦ is given by

ΔΦ = BA

ΔΦ  = μ₀nIA

ΔΦ  = 4πx10⁻⁷*8720*3.2*0.194x10⁻³

ΔΦ  = 6.802x10⁻⁶ Tm²

So the induced emf in the secondary winding is

ξ = -NΔΦ/Δt  

ξ = -5*6.802x10⁻⁶/4.472

ξ = -7.605x10⁻⁶ V

The negative sign indicates that the induced emf opposes the change that produced it in the first place.

  1.the balanced   chemical equation is as below

cu +   2 ag(no)₃ → cu(no₃)₂   +2 ag

2.the   much silver   produced   is   50.9 g

step 1: find the   moles of cu

moles =   mass÷   molar mass

  from periodic table the molar mass of cu = 63.5 g/mol

moles is therefore = 15.00 g÷ 63.5 g/mol = 0.236   moles

step 2: use the mole ratio to determine the   moles of ag

from equation above   cu: ag   is 1: 2

therefore the moles of ag   =0.236   moles   x 2/1 =0.472   moles

step 3: find the mass   of ag

mass = moles x molar mass

from periodic table   the molar mass of ag =107.87 g/mol

mass   = 0.472   moles x 107.87 g/mol = 50.9 g

3.   the   much   silver   collected worth is   1.797 oz

  convert   50.9 g   to oz

that is   1 gram = 0.0353 oz

          50.9 grams =?   oz

by cross multiplication

={(50.9 grams x 0.0353 oz) / 1   gram}   =1.797 oz