A) Double
B) half
C) four times
D) remain same
Correct Answer: D
Solution :
[D]K.E. of charge Q accelerated with potential difference of U is given by K.E. = QU |
Magnetic moment \[=i\,\,\times \,\,Area\]\[=\frac{Q}{T}\,\,\times \,\,\pi {{R}^{2}}\] |
Where T is time period of circular motion of charge Q and R is radius of circular motion |
\[\therefore T=\frac{2\pi m}{QB}\] |
\[R=\sqrt{\frac{2mKE}{QB}}=\sqrt{\frac{2mU}{QB}}\] |
Magnetic moment \[=\frac{{{Q}^{2}}\,\,\times \,\,B}{2\pi m}\times \frac{\pi \,\,\times \,\,2m\,\,\times \,\,U}{{{Q}^{2}}{{B}^{2}}}\] |
Magnetic Moment \[\propto \frac{U}{B},\] so if U and B both are double magnetic moment remain unchanged. |
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