Question

Two circular coils of radii 5 cm and 10 cm carry currents of 2 A.The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as their centres coincide.Magnitude of magnetic field at the common centre of coil is

• A. $8\pi \times {10}^{-4}T$ if currents in the coils are in same sense
• B. $4\pi \times {10}^{-4}T$ if currents in the coils are in opposite sense
• C. zero if currents in the coils are in opposite sense
• D. $8\pi \times {10}^{-4}T$ if currents in the coils are in opposite sense

Answer 1

Answer: (A), (C)

The correct options are
A $8\pi \times {10}^{-4}T$ if currents in the coils are in same sense
C zero if currents in the coils are in opposite sense

$B_1=\frac{{\mu }_o{N}_1{i}_1}{2R_1}=\frac{(4\pi \times {10}^{-7})\left(50\right)\left(2\right)}{2(5\times {10}^{-2})}$

$=4\pi \times {10}^{-4}T$

$B_2=\frac{{\mu }_o{N}_2{i}_2}{2R_2}=\frac{(4\pi \times {10}^{-7})\left(100\right)\left(2\right)}{2(10\times {10}^{-2})}$

$=4\pi \times {10}^{-4}T$
When currents are in the same direction

$B_{net}=B_1+B_2$

When currents are in the opposite direction

$B_{net}=B_1-B_2$