Question

Circle the answer

3. (10 points) Consider a conducting loop with radius a in the y:-plane centered about the origin that carries a current (a) (7 points) Use the Bjot-Savart Law to derive an expression for the magnetic field at a point P on the r-axis. (b) (3 points) Why would it be diffiult to perform the same derivation usgmpè's Laxd

Answer 1

Expression for the magnetic field at a point P on the x-axis for a current conducting loop in yz-plane Given I = current in the loop a = radius of the current carrying loop x = distance between origin and point P (on the x-axis) dl^vector = small conducting element of loop dB^vector = magnetic field at point P due to dl^vector (resultant magnetic field) dB^vector_x magnetic field along x-axis dB^vector_perpendicular magnetic field perpendicular to x-axis theta rightarrow angle between dB^vector and x-axis Bio savarats law gives that magnetic field at any point is equal to dB^vector = mu_0/4 pi I dl^vector times r^vector/r^vector^3 [perpendicular: perpendicular] where r^2 = x^2 + a^2 [Because dl^vector is perpendicular to r] so, dl^vector times r^vector = rdl^vector thus dB = mu_0/4pi I dl^vector/(x^2 + a^2) Now Because dB has two component dB_x and dB_perpendicular But dB_perpendicular is cancelled out (Because PS = PS�) so dB_x = dB cos theta