A) \[F\propto \left( \frac{{{a}^{2}}}{{{d}^{3}}} \right)\]
B) \[F\propto \left( \frac{a}{d} \right)\]
C) \[F\,\,=\,\,0\]
D) \[F\propto {{\left( \frac{a}{d} \right)}^{2}}\]
Correct Answer: D
Solution :
work done by magnetic force = fdx \[fdx=-\,dU\] \[f\,\,=\,\,-\frac{dU}{dx}\] dx \[U=-\,\overrightarrow{M}.\text{ }\overrightarrow{B}\] \[U\,\,=\,\,-\frac{{{I}_{2}}\times \pi {{a}^{2}}\,\times \,{{\mu }_{0}}{{I}_{1}}}{2\pi x}\,\,\cos \,0{}^\circ \] \[\frac{dU}{dx}\,\,=\,\,\frac{{{\mu }_{0}}{{I}_{1}}{{I}_{2}}\pi {{a}^{2}}\,\,}{2\pi }\,\,\left( \frac{1}{{{x}^{2}}} \right)\] \[f\,\,=\,\,\frac{{{\mu }_{0}}{{I}_{1}}{{I}_{2}}\pi {{a}^{2}}}{2\pi {{d}^{2}}}\,\,(put\,\,x\,\,=\,\,d)\] \[f\,\,\propto \,\,\frac{{{a}^{2}}}{{{d}^{2}}}\]You need to login to perform this action.
You will be redirected in
3 sec