Magnetic Effect of Electric Current

(1) Ampere’s Law: $∮ \ov B . \ov{dl} = μ_o I$

(2) Straight conductor: ${μ_o}/{4π} {2I}/{r}$

(3) Solenoid:

(i) B = $μ_o$ n I
(ii) Near end: ${μ_o n I}/{2}$

(4) MCG: $I = ({c}/{nBA}) θ$ c -> spring constant

(5) Sensitivity: ${dθ}/{dI} = {nBA}/{c}$

(6) Ammeter:
(i) $S = ({I_g}/{I – I_g}) G$
(ii) $S = {G}/{(n-1)}$     $n = {I}/{I_g}$

(iii) $R = ({G}/{G + S}) S$

(7) Voltmeter: $R = V/I_g – G$
R = G(n-1)     $n = {V}/{V_g}$

(8) Cyclotron:
(i) radius of +ve ion: $r = {mv}/{Bq}$
(ii) Period: $T = 2t = {2πm}/{Bq}$

(iii) Velocity: $v_{max} = {Bqr}/{m}$

(iv) $KE = {(BqR)^2}/{2m}$ in joule

(9) τ = NIAB

(10) $I_g = ({S}/{S + G}) I$

$S = ({I_g}/{I – I_g}) G$