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CET Karnataka Medical CET - Karnataka Medical Solved Paper-2003

  • question_answer
    A wire in the form of a circular loop of one turn carrying a current produces a magnetic field B at the centre. If the same wire is looped into a coil of two turns and carries the same current, the new value of magnetic induction at the centre is:

    A)  3B   

    B)  56

    C)  4B   

    D)  2B

    Correct Answer: C

    Solution :

    Magnetic field at the centre of a current carrying loop is given by \[B=\frac{{{\mu }_{0}}ni}{2{{r}_{1}}}\] Here: n = no. of turns in loop i = current,  \[{{r}_{1}}\]= radius of loop, \[{{r}_{1}}=r\] For n = 1 turn                                 \[B=\frac{{{\mu }_{0}}i}{2{{r}_{1}}}\]                   ??.(1)                When   n = 2   turns   and   radius   \[{{r}_{2}}=\frac{r}{2},\,\,{{i}_{2}}=i\]                                           \[{{B}_{2}}=\frac{{{\mu }_{0}}\times 2\times i}{2\left( \frac{r}{2} \right)}\]                or                      \[{{B}_{2}}=\frac{2{{\mu }_{0}}i\times 2}{2r}\]                     ??(2) Now, from eqn. (1) and (2)                            \[\frac{{{B}_{2}}}{B}=4\] Hence,  \[{{B}_{2}}=4B\]


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