A) \[12.6\times {{10}^{-3}}\,Weber/{{m}^{2}},\ 6.3\times {{10}^{-3}}\,Weber/{{m}^{2}}\]
B) \[12.6\times {{10}^{-3}}\,Weber/{{m}^{2}},\ 25.1\times {{10}^{-3}}\,Weber/{{m}^{2}}\]
C) \[25.1\times {{10}^{-3}}\,Weber/{{m}^{2}},\ 6.3\times {{10}^{-3}}\,Weber/{{m}^{2}}\]
D) \[25.1\times {{10}^{-5}}\,Weber/{{m}^{2}},\ 6.3\times {{10}^{-5}}\,Weber/{{m}^{2}}\]
Correct Answer: C
Solution :
The magnetic field in the solenoid along its axis (i) At an internal point\[={{\mu }_{o}}ni\] \[=4\pi \times {{10}^{-7}}\times 5000\times 4=25.1\times {{10}^{-3}}Wb/{{m}^{2}}\] \[(\text{Here }n=50\,turns/cm=5000\,turns/m)\] (ii) At one end \[{{B}_{end}}=\frac{1}{2}{{B}_{in}}=\frac{{{\mu }_{0}}ni}{2}=\frac{25.1\times {{10}^{-3}}}{2}\]\[=12.6\times {{10}^{-3}}Wb/{{m}^{2}}\]
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