Determine the magnetic field (in terms of I, a , and d ) at the origin due to th

Question

Determine the magnetic field (in terms of I, a, and d) at the origin due to the current loop shown in Figure P30.14. (Use mu_0 for

A principal hires an agent to perform a certain task. The revenues from this task depend completely on the agenf s hours of effort, which the principal does not observe. The agent's cost of incurring effort is given by: c(e) = 0 if e=100 The marginal cost of effort corresponding to the function above is 2*(e - 100). Every hour of the agent's effort generates $50 in revenues for the principal. Meanwhile the agent's next best alternative is to work at a neighboring firm, where he will not need to incur any effort and can earn a guaranteed salary of $800. Suppose the principal decides to give the agent a 40% commission. How much should he offer in addition as a fixed salary? What is the optimal contract, consisting of a fixed salary and a commission, that the principal should offer the agent? How much higher is the principal's profit in (b) than in (a)? Question 2: There are twro types of consumers in a given market: Type A and Type B, with the following demand curves for the product: Pa = 120 - 2*Qa Pb = 204 - 5*Qb The market is served by a monopolist with a constant marginal cost of $4 What is the profit-maximizing price for the monopolist if it cannot tell the two types of customers apart? What are the profit-maximizing prices if the monopolist can distinguish the two types and charge them different prices? How much higher is the monopolist's profit in (b) than in (a)?

Explanation / Answer

The field of the vertical sections of the wire cancels each other since they are simmetrical from the origin and have oppsing currents. it remains only the horizontal portion of the wire.

B=mu_0*I/(4*pi*d)*(cos(theta1) +cos(theta2))

here theta1,2 are the angles under which the the point O is seen from the ends of the wire.

cos(theta1)=cos(theta2) =a/sqrt(a^2+d^2)

Hence

B = mu_0*I/(4*pi*d)*2*a/sqrt(a^2+d^2)

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