Magnetic Induction of a Current-Carrying Long Straight Wire Magnetic Induction of a Current-Carrying Long Straight Wire
a) Derive an expression for the magnetic field B at a point of distance r, from an infinitely long wire that carries a current I. Your derivation should include the direction of the magnetic field with respect to the direction of current flow. Verify your expression by using the experimental results obtained. If your results do not show the expected relationship, explain why.
In order to derive an expression for the magnetic field B at a point of distance r, from an infinitely long wire that carries a current I, we can refer to fig. 10. From symmetry, B must be constant in magnitude and parallel to ds at every point on this circle. Therefore if the total current passing through the plane of the circle is I, from Ampere’s law,
= = B (2r) = µ0I (for r ≥ R)
Based on the expression derive, when all other variables are kept constant, it can be shown that,
B∝
Therefore as the point of distance r increases, the magnitude of the B field will decrease accordingly. This can be verified based on the data collected in Data Table 2. It had shown that as increases, the voltage increases as well. By using the data collected, we are able to plot a best fit straight line graph (as shown in Appendix 2: Laboratory Log Sheet 2). Hence we are able to verify that field is inversely proportional to r.
b)Derive and comment on the dependence of the induced voltage in the inductor coil on the (i) frequency and (ii) magnitude of the ac current flowing in the long wire. Verify your answers by using the experimental results obtained. If your results do not show the expected relationships, explain why.
From the experiment that had been done, an AC circuit consisting of an inductor coil is connected to the terminals of an AC current source ∆v. We can also refer to fig. 11 as a simple diagram used to illustrate the experimental setup that was done previously.
∆v = ∆Vmax
From Kirchhoff’s loop rule,
∆v - ∆vL = 0
∆vL = ∆Vmax where ∆vL is the
In order to derive an expression for the magnetic field B at a point of distance r, from an infinitely long wire that carries a current I, we can refer to fig. 10. From symmetry, B must be constant in magnitude and parallel to ds at every point on this circle. Therefore if the total current passing through the plane of the circle is I, from Ampere’s law,
= = B (2r) = µ0I (for r ≥ R)
Based on the expression derive, when all other variables are kept constant, it can be shown that,
B∝
Therefore as the point of distance r increases, the magnitude of the B field will decrease accordingly. This can be verified based on the data collected in Data Table 2. It had shown that as increases, the voltage increases as well. By using the data collected, we are able to plot a best fit straight line graph (as shown in Appendix 2: Laboratory Log Sheet 2). Hence we are able to verify that field is inversely proportional to r.
b)Derive and comment on the dependence of the induced voltage in the inductor coil on the (i) frequency and (ii) magnitude of the ac current flowing in the long wire. Verify your answers by using the experimental results obtained. If your results do not show the expected relationships, explain why.
From the experiment that had been done, an AC circuit consisting of an inductor coil is connected to the terminals of an AC current source ∆v. We can also refer to fig. 11 as a simple diagram used to illustrate the experimental setup that was done previously.
∆v = ∆Vmax
From Kirchhoff’s loop rule,
∆v - ∆vL = 0
∆vL = ∆Vmax where ∆vL is the