# Magnetic Field , Self-inductance & energy Question

by Fazza3_uae
Tags: energy, field, magnetic, selfinductance
 P: 51 1. The problem statement, all variables and given/known data Given: μ0 = 4 π x10−7 T.m/A. An air-core circular solenoid is shown in the figure below. A current of 22 A is establishedin the wire which makes up this solenoid. http://img412.imageshack.us/i/81565602.jpg/ a) What is the magnetic field at its center? [[ Answer in units of T ]] b) What is its self-inductance? [[ Answer in units of mH ]] c) How much energy is stored in the solenoid? [[ Answer in units of J ]] d) A tight circular loop whose diameter is less than the diameter of the solenoid (as shownin the figure below) is concentric with the solenoid and is placed midway along the length of the solenoid. Starting from t = 0, the initial current increases linearly in time until the current doubles in 5 s, and then the current remains constant at 44 A. Find the magnitude of the emf |ε| in the circular loop at a time t, 0 s < t < 5 s, during the increase of current. [[ Answer in units of V ]] http://img142.imageshack.us/i/96025878.jpg/ 2. Relevant equations Faraday's Law V = N d$$\phi$$/dt Self induction = - L di/dt Energy Stored in magnetic field = 0.5 L I2 $$\epsilon$$ = -NACos$$\theta$$ dB/dt Magnetic field for an ideal selenoid = μ0 i n 3. The attempt at a solution for part a ) do i have to just plug in the values in the magenetic field equation ?? B = μ0 i n μ0 is Given n is given & i is given For part b ) how to find di/dt ? for part c ) every thing is given do i have to insert the values and that is it ?? part d ) no idea how to start so any clue or hint will be appreciated. thx in advance.