1) A 250 mA current flows through a circular arc that subtends 130 degrees at th

Question

1) A 250 mA current flows through a circular arc that subtends 130 degrees at the center point P. The radius of the arc is 3.48 m. What is the strength of the magnetic field at the center of the arc?

2) A short coil of five loops having a common radius of 5.50 cm conducts a current of 1.20 A. The loops are tightly wrapped so that they can be considered to be in the same place. (a) What is the strength of the central magnetic field? (b) What current would have to flow through a single loop of wire of the same radius to produce the same magnetic field?

3) A certain helix in three-dimensional space is described by the equations x = cos , y = sin , and z = . Calculate the line integral, along one loop of this helix, of the dot product V·ds, where V is the constant vector field (3, 5, 4) and ds = (dx, dy, dz).

a) 0 b) 2pi c) 4pi d) 8pi

Explanation / Answer

1) magnetic filed due to a cilcular arc at the center, B = (theta/360)*mue*I/(2*R)

here, theta is the angle subtended by the arc at the center,

mue is permeability of free space = 4*pi*10^-7

I is current

R is radius

so,

B = (130/360)*(4*pi*10^-7*250*10^-3/(2*3.48))

= 1.63*10^-8 T or 16.3 nT

2)

a) B = N*mue*I/(2*R)

= 5*4*pi*10^-7*1.2/(2*0.055)

= 6.85*10^-5 T

b) 5 times. i.e 6 A

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