Saved Bookmarks
| 1. |
Consider an infinitely long wire carrying acurrent I(t), with (dI)/(dt)=lambda =constant. Find the dt current produced in the rectangular loop of wire ABCD if its resistance is R as in figure. |
|
Answer» Solution :Consider small area ELEMENT having thickness dr and length l on closed rectangular loop ABCD at distance l from very long current carrying wire as shown in FIGURE. Magnetic field at this STRIP, due to very long current carrying wire, `B=(mu_0I)/(2pir)` (Outside the plane) Magnetic flux linked with this strip, `d phi=Bda=Bldr` `d phi=(mu_0 I ldr)/(2pir)` Net flux linked with ABCD loop, `phi=int_(x_0)^x (mu_0Il)/(2pir)dr` `=(mu_0Il)/(2pi)[ln R]_(x_0)^x` `phi=(mu_0Il)/(2pi)ln (x/x_0)` Induced emf, `epsilon=(dphi)/(dt)=d/(dt)[(mu_0Il)/(2pi) ln (x/x_0)]` `=(mu_0l)/(2pi) ln (x/x_0)(dI)/(dt)` `epsilon=(mu_0l lambda)/(2pi) ln (x/x_0) (because (dI)/(dt)=lambda)` Induced current, `I=epsilon/R=(mu_0llambda)/(2piR)ln (x/x_0)` |
|