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A flat circular coil which has 𝑁 turns each of diameter d carries a current 𝐼. If 𝜇0 is the permeability of free space, what is the expression of magnetic field 𝐵 at the center of the coil?

Determine the percentage yield of Carbon, when 0.5 mole of Sucrose is decomposed and 70.0 g of C was collected during the experiment. Equation: C12H22O11 = 12 C + 11H2O

Let η and ξ be two independent normal random variables with mean 1 and variance 2. Which of the

following statements is correct?

◦ η + ξ and η − ξ are uncorrelated and independent

◦ η + ξ and η − ξ are uncorrelated, but not independent

◦ η + ξ and η − ξ are correlated, but independent

◦ η + ξ and η − ξ are correlated and not independent

◦ None of the statements is correct

You titrate 100.0 mL of a 0.025 M solution of benzoic acid with 0.100 M NaOH to the equivalence point. What is the Ph when half the of the benzoic acid has been consumed? C6H5CO2H + NaOH -> Na+ + C6H5CO2- + H2O. Provide answer with solution.

What is the kinetic energy of automobile with a mass of 1.25 x 10^3 kg traveling at a speed of 10.0m/s

You add 200.0 mL of 0.10 M KOH to 50.0 mL of 0.40 M HF. What is the pH of the resulting solution? Provide answer with solution.

A square metal plate with a length af0.20 m and with a charge of 9.7x 10 C.

Find the electric field of the square metal plate.

You add 100.0 mL of 0.50 M NaOH to 50.0 mL of 1.00 M NH4Cl. What is the pH of the resulting solution? Kb(NH3) = 1.8 x 10^-5. Provide answer with solution.

A manufacturer wants to build a spring that takes a force 10 N (in negative direction) to compress it 0.2 m from the equilibrium position. The spring should be able to stretch 0.5 m from the equilibrium position.

As a mechanical engineer, you were asked to present how much work should be done to stretch the spring.The presentation shall include important components of the problem, complete and correct computations and a logical and organized explanation.


First, create a force function F(x) by finding the spring constant k in F(x) = kx where F(x) is the force and x is the position from the equilibrium.

Then, calculate work ustng the concept of the definite integral.

If a variable force F(x) moves an object in a positive direction along the x-axis from point a to point b, then the work done on the object is W = ∫ ^b a F(x) dx

You mix 100.0 mL of 0.20 M HBr and 50.0 mL of 0.40 M NaClO. What is the pH of the resulting solution? Ka(HClO) = 3.5 x 10^-8. Provide your answer with solution.

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