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A long cylidrical conductor of radius `R` carries a current i as shown in figure. The current desity `J` is a function of radius according to `J=br`, where `b` is a constant. Find an expression for the magnetic field `B` a. at a distasnce `r_1ltR` and b.at a distance `r_2gtR,` measured from the axis. |
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Answer» Correct Answer - B::C `i=int_0^r(2pir dr)j=int_0^r(2pir dr)(br)=(2pibr^3)/3` `a. For r_1ltR` `B=mu_0/(2pi) i_m/r_1` `=mu_0/(2pi) ((2pibr_1^3/3)/r_1)` `=(mu_0br_1^2)/3` b. For `r_2ltR` `B=mu0/(2pi) i_m/r_2` `=(mu_0)/(2pi) ((2pibR^3/b)/r_2)=(mu_0bR^30/(3r_2)` |
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