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4. Moving charges and magnetism — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics4. Moving charges and magnetism1 Mark
MCQ
Two circular loops having same radius $[ R =10\, cm ]$ and same current $\frac{7}{2} A$ are placed along same axis as shown. If distance between their centre is $10\, cm$, find net magnetic field at of point $P.$
  • A
    $\frac{50 \mu_{0}}{\sqrt{5}} T$
  • B
    $\frac{28 \mu_{0}}{\sqrt{5}} T$
  • ✓
    $\frac{56 \mu_{0}}{\sqrt{5}} T$
  • D
    $\frac{56 \mu_{0}}{\sqrt{3}} T$
✓

Answer

Correct option: C.
$\frac{56 \mu_{0}}{\sqrt{5}} T$
c
Both the coils have same magnetic field,

$B_{1}=B_{2}$

At point $P$

The magnetic field will be in same direction by both coils,

$B=B_{1}+B_{2}$

$=B_{1}+B_{1}$

$=2 B_{1}$

The magnetic field at point $P$ is,

$B=2\left(\frac{\mu_{0} i r^{2}}{2\left(r^{2}+n^{2}\right)^{3 / 2}}\right)$

$=\frac{\mu_{0} i r^{2}}{2\left(r^{2}+n^{2}\right)^{3 / 2}}$

Substitute the values in the above equation.

$B=\frac{\mu_{0} \times \frac{7}{2} \times 0.1^{2}}{2\left(0.1^{2}+0.05^{2}\right)^{3 / 2}}$

$=\frac{56 \mu_{0}}{\sqrt{5}} T$

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