Magnetic Effects Of Current Question 24
Question: The magnetic field $ d\overrightarrow{B} $ due to a small current element $ d\overrightarrow{l,} $ at a distance $ \overrightarrow{r,} $ and element carrying current i is, or Vector form of Biot-savart’s law is [CBSE PMT 1996; MP PET 2002; MP PMT 2000]
Options:
A) $ d\overrightarrow{B}=\frac{{\mu_{0}}}{4\pi }i,( \frac{d\overrightarrow{l,}\times \overrightarrow{r,}}{r} ) $
B) $ d\overrightarrow{B}=\frac{{\mu_{0}}}{4\pi }i^{2},( \frac{d\overrightarrow{l,}\times \overrightarrow{r,}}{r} ) $
C) $ d\overrightarrow{B}=\frac{{\mu_{0}}}{4\pi }i^{2},( \frac{d\overrightarrow{l,}\times \overrightarrow{r,}}{r^{2}} ) $
D) $ d\overrightarrow{B}=\frac{{\mu_{0}}}{4\pi }i,( \frac{d\overrightarrow{l,}\times \overrightarrow{r,}}{r^{3}} ) $
Show Answer
Answer:
Correct Answer: D
Solution:
$ dB=\frac{{\mu_{0}}}{4\pi }\cdot \frac{idl\sin \theta }{r^{2}} $
Þ $ d\overrightarrow{B}=\frac{{\mu_{0}}}{4\pi }\cdot \frac{i,(d\overrightarrow{l,}\times \overrightarrow{r,})}{r^{3}} $
BETA
