A) \[c:1\]
B) \[{{c}^{2}}:1\]
C) \[1:1\]
D) \[\sqrt{c}:1\]
Correct Answer: C
Solution :
| Option [c] is correct. |
| Explanation: Average energy by electric field |
| \[{{\operatorname{E}}_{0}}\] is \[{{\operatorname{U}}_{av}}\] |
| \[{{\operatorname{U}}_{av}}=\frac{1}{2}{{\varepsilon }_{0}}E_{0}^{2}\] |
| But \[{{\operatorname{E}}_{0}}={{\operatorname{cB}}_{0}}\] |
| \[{{({{\operatorname{U}}_{av}})}_{\operatorname{electric}\ field}}=\frac{1}{2}{{\varepsilon }_{0}}{{(c{{B}_{0}})}^{2}}=\frac{1}{2}{{\varepsilon }_{0}}{{c}^{2}}\operatorname{B}_{0}^{2}\] |
| \[=\frac{1}{2}{{\varepsilon }_{0}}.\frac{1}{{{\mu }_{0}}{{\varepsilon }_{0}}}{{({{B}_{0}})}^{2}}\because {{c}^{2}}=\frac{1}{{{\mu }_{0}}{{\varepsilon }_{0}}}\] |
| \[{{({{u}_{av}})}_{\operatorname{electric}\ field}}=\frac{1}{2{{\mu }_{0}}}B_{0}^{2}{{({{\operatorname{U}}_{av}})}_{(magnetic\ field)}}\] |
| \[\operatorname{Ratio}=\frac{({{\operatorname{U}}_{av}})\operatorname{electric}\ field}{({{\operatorname{U}}_{av}})(magnetic\ field)}\] |
| \[=\frac{1}{1},i.e.,1\ :1\] |
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