# Problem: a.) Consider a circular current loop of radius 10.5 cm with 200 total turns. Assume that the current though the coil is I. What is the magnitude of the magnetic field at the center of the coil? ( Your answer should be a numerical value multiplied by the current I)b.) A time varying current of the form I(t) = I_0sin(2*pi*f*t) is passed through the circular coil in part a) where I_0 = 10mA. using your result from a), write down the expression for the time varying magnetic field B(t) at the center of the coil.c.) A small 1.5 cm radius circular current loop is placed at the center of the large current loop from part a) oriented so that the plane of the current loop is perpendicular to the magnetic field. Assume that the magnetic field from the large current loop is constant over the small loop. What is the magnetic flux through the small current loop? (use your result from part b)d.) What is the total induced emf in the small current loop assuming that it has 2000 turns? (use your result from part c) The frequency of the time varying current is f = 1000 Hz. (Your answer should be in the form of a numerical value times a trigonometric function of 2*pi*f*t)

###### FREE Expert Solution

a.)

The magnetic field produced by a current loop:

$\overline{){\mathbf{B}}{\mathbf{=}}{\mathbf{N}}\frac{{\mathbf{\mu }}_{\mathbf{0}}\mathbf{i}}{\mathbf{2}\mathbf{r}}}$

B = Nμ0i/2r = (200)(4π × 10-7)(i)/(2 × 0.105) = (1.20 × 10-3)i

###### Problem Details

a.) Consider a circular current loop of radius 10.5 cm with 200 total turns. Assume that the current though the coil is I. What is the magnitude of the magnetic field at the center of the coil? ( Your answer should be a numerical value multiplied by the current I)

b.) A time varying current of the form I(t) = I_0sin(2*pi*f*t) is passed through the circular coil in part a) where I_0 = 10mA. using your result from a), write down the expression for the time varying magnetic field B(t) at the center of the coil.

c.) A small 1.5 cm radius circular current loop is placed at the center of the large current loop from part a) oriented so that the plane of the current loop is perpendicular to the magnetic field. Assume that the magnetic field from the large current loop is constant over the small loop. What is the magnetic flux through the small current loop? (use your result from part b)

d.) What is the total induced emf in the small current loop assuming that it has 2000 turns? (use your result from part c) The frequency of the time varying current is f = 1000 Hz. (Your answer should be in the form of a numerical value times a trigonometric function of 2*pi*f*t)