## Moving charges and magnetism

# Moving Coil Galvanometer

- Current in MCG \tt i = \frac{C \theta}{BAN}
- Current sensitivity \tt Si = \frac{BAN}{C}
- Voltage sensitivity \tt SV = \frac{\theta}{iG} = \frac{BAN}{CG}
- MCG can measure current up to 10
^{−9}Amp. - Shunt is a low resistance connected in parallel to galvanometer to protect from large current.
- R Equivalent = \tt \frac{GS}{G + S}

G = Galvanometer resistance , S = Shunt resistance - V = iReq = \tt i \frac{GS}{G+S}
- V = ig G = is S.
- Ammeter is an instrument used to measure current
- Shunt resistance \tt S = \frac{G}{\left(\frac{i}{ig} - 1\right)}
- Ammeter must always be connected in series in the circuit.
- Galvanometer can be converted in to Ammeter by connecting a shunt in parallel.
- Galvanometer can be converted in to voltmeter by connecting high resistance in series.
- V = ig (G + R)
- Voltmeter is used to measure potential difference across the elements in the circuit.
- Resistance of a voltmeter is very high.
- Among low range and high range voltmeter high range voltmeter has more resistance.
- Equivalent resistance of voltmeter = G + R
- Resistance to be connected in series \tt R = \frac{V}{ig} - G
- Tangent galvanometer works on the principle of B = B
_{H}Tanθ - Magnetic induction at the centre of loop = \tt \frac{\mu_0ni}{2r}
- \tt i=\left(\frac{2rB_H}{\mu_0n}\right)\tan \theta
- Reduction factor \tt K=\left(\frac{2rB_H}{\mu_0n}\right)
- Tangent galvanometer cannot be used at magnetic poles
- Tangent galvanometer can measure current upto 10
^{−6}A - Magnetic moment of a current of length L wire bent in the form of a circle is \tt \frac{iL^2}{4\pi}
- Magnetic field at the centre of loop is \tt B=\left(\frac{\pi -\theta}{\pi}\right)\frac{\mu_0i}{2a}
- Magnetic field at the centre \tt B=\frac{\mu_0i}{2\pi r}\left(\pi -\phi+\tan\phi\right)
- Magnetic induction at point o \tt B=\frac{\mu_0i}{4r}\left[\frac{3}{2}-\frac{1}{\pi}\right]
- Cyclotron is a machine to accelerate charged particles.
- Principle of cyclotron is frequency of revolution of charged particle in a magnetic field is independent of its energy.
- Centripetal force in cyclotron \tt F=\frac{mv^2}{r}=Bqv
- Radius of circular path \tt r=\frac{mv}{Bq}
- Time period of charged particle \tt T=\frac{2\pi m}{Bq}
- Frequency of charged particle \tt f=\frac{Bq}{2\pi m}
- KE of charged particle =\tt \frac{1}{2}\frac{B^2q^2r^2}{m}
- Use Amperes Right hand grip rule to find the direction of magnetic lines of force around current carrying conductor.
- Use Fleming's left hand rule to know the direction of O force when charge particle moving in magnetic field.
- Magnetic field at p is zero.
- The net force at O is zero.
- Magnetic field induction at 'O' is \tt B=\frac{\mu_0i}{4\pi}\left(\frac{3\pi}{4x}+\frac{\sqrt 2}{2y}\right)
- Magnetic induction at p is \tt B=\frac{\mu_0i}{2\pi r}\left(1+\sqrt2\right)
- Magnetic induction at 'O' is\tt B=\frac{\mu_0}{4\pi}\frac{i}{R}\left(\pi +1\right)
- Magnetic induction at O is \tt B=\frac{\mu_0i}{2r}\left(\frac{\pi}{2\pi}\right)=\frac{\mu_0i}{4r}

### View the Topic in this video From 02:15 To 20:53

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1. In moving coil galvanometer the current I passing through the galvanometer is directly proportional to its deflection (θ).*I* ∝ θ or, *I* = *G*θ

where G = \frac{k}{NAB} = galvanometer constant

2. **Current sensitivity :** It is defined as the deflection produced in the galvanometer, when unit current flows through it.

I_{s} = \frac{\theta}{I} = \frac{NAB}{k}

3. **Voltage sensitivity :** It is defined as the deflection produced in the galvanometer when a unit voltage is applied across the two terminals of the galvanometer

V_{s} = \frac{\theta}{V} = \frac{\theta}{IR} = \frac{NAB}{kR}