(a) Write an expression of magnetic moment associated with a current (I) carrying circular coil of radius r having N turns.
(b) Consider the above mentioned coil placed in YZ plane with its centre at the origin. Derive expression for the value of magnetic field due to it at point (x, 0, 0).
OR
(a) Define current sensitivity of a galvanometer. Write its expression.
(b) A galvanometer has resistance G and shows full scale deflection for current Ig .
(i) How can it be converted into an ammeter to measure current up to I0 (I0 > Ig ) ?
(ii) What is the effective resistance of this ammeter ?

Question

(a) Write an expression of magnetic moment associated with a current (I) carrying circular coil of radius r having N turns.
(b) Consider the above mentioned coil placed in YZ plane with its centre at the origin. Derive expression for the value of magnetic field due to it at point (x, 0, 0).
OR
(a) Define current sensitivity of a galvanometer. Write its expression.
(b) A galvanometer has resistance G and shows full scale deflection for current Ig .
(i) How can it be converted into an ammeter to measure current up to I0 (I0 > Ig ) ?
(ii) What is the effective resistance of this ammeter ?

Infinity Learn · Accepted Answer

(a) magnetic moment =M=NIAM=NIπr2According to Biot-sevart law, dB→=μoI4π|dl×r→|r3 dB→=μoI4πdlr2dB⊥ components due to diametrically opposite components cancel out. Only 𝑑𝐵𝑥 components refraindBx=μ0Idl4πr2⋅cos⁡θB=∫dBxB=μ0IR22R2+x23/2 (along x axis) ORa) Deflection per unit currentIs=θI=BNAKb) (i) By connecting a low resistance (Rs) in parallel to galvanometer such thatI0-IgRs=IgG(ii) effective resistance 1RA=1RS+1G=G+RSRSG∴RA=RSGG+RS

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