Q. Applying Biot-savart’s law deduce the expression the for the magnetic field at center of a semiconductor loop of radius R carrying current (BSEB-2009) .

 Answer : i dL 900 R 0 dB let, there is a semiconductor current carrying circular coil of radius R carrying current i. dL is an small element of the circular coil. The magnetic field at 0 of the coil due to the small element dL is dB. A/C to Biot-sevart law 𝒅𝑩 = 𝝁𝟎 4𝜋 × 𝑰𝒅𝑳𝒔𝒊𝒏𝟗𝟎 𝑹𝟐 𝒅𝑩 = 𝝁𝟎 4𝜋 × 𝑰𝒅𝑳 𝑹𝟐 ----------(1) Now , magnetic field due to the whole semiconductor coil . 𝑩 = ∫𝒅𝑩 = ∫ 𝝁𝟎 𝟒𝝅 × 𝑰𝒅𝑳 𝑹𝟐 𝝅𝑹 𝟒𝝅 = 𝝁𝟎 4𝜋 × 𝑰 𝑹𝟐 ∫ 𝒅𝑳 = 𝝁𝟎 4𝜋 × 𝑰 𝑹𝟐 [𝑳]𝟎 𝝅𝑹 𝝅𝑹 𝟎 = 𝝁𝟎 4𝜋 × 𝑰 𝑹𝟐 [𝜋𝑅 − 0] = 𝝁𝟎 4𝜋 × 𝑰 𝑹𝟐 × 𝜋𝑅 𝑩 = 𝝁𝟎𝑰 4𝜋 This magnetic field at the center of circular coil .