Ampere\'s Law . This question explores the relationship between the strenght of

Question

Ampere's Law. This question explores the relationship between the strenght of a magnetic field and the current which produces it.

b. Calculate the area of the shaded region in Figure 3. (Hint: Break the region into simple shapes, like triangles and rectangles.)

Area under the curve = ________G.m

c. The solenoid carries 10 A of current and has 10 turns. Calculate Ienc, the cureent enclosed by detector's path. (Hint: Consider how many coils are inside the path and how much current flows through each coil.)

Ienc = ______ A

d. Ampere's law tells us that the area you found above will be proportional to the current passing through the loop. Matematically we could say:          Area under the curve = u0 Ienc , where u0 is a constant.

Using the area you found on part (b) and enclosed current you found in part (c), calculate a value for u0. Does your number agree with the value for u0 given in the lab manual (u0= 1.26x10-2 G.m/A)?

To understand what this means, we imagine sliding the detector through a circular loop, following the field line, as in Figure 2. A (very) simplified plot of the detected axial component vs. the distance around the loop is shown in Figure 3. Calculate the area of the shaded region in Figure 3. Area under the curve = Gm

Explanation / Answer

b) area = area of bottom rectangle + area of upper triangle = 1*0.2 + 0.5*0.2*10.6 = 1.26 G-m

c) Ienc = no. of turns X current in one turn = 100 A

d) Integral of B.dL = mu_not * enclosed current. This gives mu_not = 1.26 / Ienc = 1.26 E -2 which is exactly equal to lab manual value.

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