Now consider a uniform magnetic field pointing to the right of the page and at a
ID: 2078523 • Letter: N
Question
Now consider a uniform magnetic field pointing to the right of the page and at an angle of 45 degree into the plane of the page, as shown. A compass is again placed in the plane of the page in the middle of the field and the needle comes to rest. In what direction will the compass needle face? Is this the true direction of the magnetic field? Why or why not? How can we adjust the compass so that we are measuring the true direction of the magnetic field? Magnetic field configuration for part (e). In this picture the page is viewed edge-on from the bottom of the page. To get a better three-dimensional picture of what the magnetic field is doing, place a sheet of paper flat on the table. Take a pen and lie it horizontally flat on the page, with the tip of the pen pointing to the right. Now take the base of the pen and lift it up. The pen is now pointing in a similar orientation as the magnetic field depicted in the above diagram. Magnitude Instead of just finding the magnitude of the magnetic field all at once, we will usually have to make do with finding the various components of the magnetic field (instead of talking about the magnitude and direction of a vector, it is often convenient to talk about the x-, y-, and z-components of the vector). The Earth's magnetic field doesn't just point from the south geographic pole to the north geographic pole along the surface, but it actually makes an angle with the surface. At the magnetic south pole, the magnetic field points vertically down into the earth. At the equator, it points completely horizontally, and at latitudes in between, it points slightly into the earth at greater and greater angles as you near the pole. f) When we do this lab, will the Earth's magnetic field point out of the earth or into the earth? g) Suppose the magnetic field from part (e) had a magnitude of 5 mu T. If we were to measure the z-component of the magnetic field, where the z-direction is the direction out of the page, or vertically up in the figure from part (e), of the magnetic field, what answer would we get? What about the x-component (where the r-direction is the direction to the right in the plane of the page)? The y-component (where the y-direction is the direction to the top in the plane of the page)? We can measure the component of the magnetic field along any direction we want. h) Suppose the magnetic field from part (e) had a magnitude of 5 mu T. If we were to measure the "to the right and into the page"-component (the direction of the field lines shown in the figure on the previous page) of the magnetic field, what answer would we get? What about 0the "to the right and out of the page"-component (where the direction is pointing to the upper-right corner rather t previous page)?Explanation / Answer
e)
The compass will align to the horizontal component of the applied magnetic field which will be diferent from the true direction of the magnetic field as in the case of magnetic inclination or dip. Usually manufactures add a special wight to balance the effect by magntic dip. In this case the dip can be measured by keeping the compass vertically and measuring the degree of change.
f) It depends on your location on the earth surface. If you are in the northern hemisphere it points above from the surface and in the southern hemisphere it goes into the surface.
g) The z component will be measured at zero. The applied magnetic field can be calculated in the x and y directions.
On x direction Mx = 5 cos 45o = 3.53 uT
On y direction My = 5 Sin45o = 3.53 uT
h) Mi = Mxcos45 i + Mysin45 j
|Mi| = 2.5 uT
Mo = Mysin45 j + Mzcos 135 k
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