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Explain, using a laballed diagram, the principal and working of a moviong coil galvnometer. What is the function of (i) unifrom radial magnetic field (ii) soft iron core ? Define the terms (i) current sensitivity and (ii) voltage sensitively of a galvanmeter. why does increasing the current sensitivity notneessarily increases voltage sensitivity ? OR (a) Write, using Biot-Savart law, the expression for the magnetic field vecB due to an element vecdl carrying current I at a distance vecr from it in a vector form. Hence ,derive the expression for the magnetic field due to a current carring loop of radius R at a point P distant x from its centre along the axis of the loop. (b) Explain how Biot- Savart law enables one to express the Ampere,s cicuital law in the integral from , vizointvecB, vec(dl) = mu_(0)I Where I is total current passing through the surface. |
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Answer» Solution :(i) Current sensitivity : The current sensitivity of galvanometer is defined as the amount of deflection produced in the galvanomter when unit current is PASSED through it. ` I = C/(NBA) phi amp` Thus, current sensitivity ` I_(s) =phi/I or , I_(s) = (NBA)/C = 1/k` The reciprocal of current sensitivity is known as figure of merit of the galvanometer . it is defined as the current which will produce deflection of one scale division. Method of Increasing current sensitivity : from above, the current sensitivity is proportional to ` (NBA)/C` Thus, the sensitivitymay be increased be increased in the following ways- (i) By increasing the Number of Turns ` N to ` but N cannot be increased indenfinitely magnets ofthe resistance of instrument . (ii) By incresing the Field` B to ` this is achieved by using powerful permanet magnets of cobalt-steel and by putting a soft-iron core which CONCENTRATES the lines of FORCE. Voltage sensitively : The voltage sensitivity of a gavanometer is defined as the amount of deflection produced in the galvenometer when a unit voltage is applied across the two terminals of the galvanometer. Voltage sensitivity = `phi/V` This value is independent of number of term N as its effect is cancelled out by the corresponding increase int he resistance of the galvanometer `C_(1)` . The unit of voltage sensitivity is division`V^(-1)` (a) According to Biot-Savart law,the magnetic field due to a current element `vec(dl)` at eh observeation point whose position vector ` vecr ` is given by ` vec(dB) = (mu_(0)I)/(4pi) . (vec(dl)xxvecr)/r^(3) , " where " mu_(0)`is the permeability of free space. Consider a circular LOOP of wire of radius r carrying a current I. Consider a current element di of the loop. The direaction of dl is along the tangent so ` dl bot r` , from Biot - Savart law, magnetic field at the centre O due to this current element is ` dB= (,mu_(0)I)/(4pi) (dlsin90^(@))/r^(2) = (mu_(0)I)/(4pi) (dl)/r^(2)` The magnetic field due to all such current elements will point into the plane of paper at the centre O. Hence the total magneic field at the centre O is .  `b=intdB=int(mu_(0)Idl)/(4pir^(2)) intdl=(mu_(0)I)/(4pir^(2)).l=(mu_(0)I)/(4pir^(2)) .2pir or B=(mu_(0)I)/(2r)` For a coilof N turns, `B=(mu_(0)NI)/(2r)` (b) Ampere's ciruital law gives relationship between line intergral of magnetic field `vecB` and total current I producing magnetic field. |
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