Param Himalaya - परम हिमालय

Principle of Homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same.  This principle is helpful because 1. To convert a physical quantity from one system of units to another :  This is based on the fact that the product of the numerical values (n) and its corresponding unit (u) is a constant,  nu = constant $n_{1} u_{1} = n_{2} u_{2}$ Consider a physical quantity which has dimension ‘a’ in mass, ‘b’ in length and ‘c’ in time. If the fundamental units in one system are $M_{1}$, $L_{1}$ and $T_{1}$ and the other system are $M_{2}$ , $L_{2}$ and $T_{2}$ respectively, then we can write $n_{1}[M_{1}^{a} \ L_{1}^{b} \ T_{1}^{c}]=n_{2}[M_{2}^{a} \ L_{2}^{b} \ T_{2}^{c}]$ 2. The magnitude of physical quantities may be added together or subtracted from one another only if they have the same dimensions. For Example, in the physical expression $v^{2} = u^{2} + 2as$, the dimensions of $v^{2}$, $u^{2}$ and 2as are...

State and Explain Lorentz Force ? - Electric force and Magnetic force - Param Himalaya Lorentz Force : when a charged particle having charge q moves in a region , where both electric field $\overrightarrow{E}$ intensity and magnetic field $\overrightarrow{B}$ exist , it experiences a net force called Lorentz Force $\overrightarrow{F}$. Lorentz Force ,$\overrightarrow{F}$ = Force on charge due to electric field + Force on charge due to magnetic field  $$\overrightarrow{F}= \overrightarrow{F_{e}} +\overrightarrow{F_{m}}$$ (i) Electric Force ( $\overrightarrow{F_{e}}$) , A charged particle having charge q placed in an electric field $\overrightarrow{E}$ experience a force given by ,  Electric force - param Himalaya $$\overrightarrow{F_{e}} = q.\overrightarrow{E}$$ Direction of this force is same is same as that of electric field $\overrightarrow{E}$. (ii) Magnetic force ($\overrightarrow{F_{m}}$) :  Magnetic force Magnetic force on a charge q moving with velocity $\overright...

Hans Christian Oersted performed a simple experiment to demonstrate the magnetic effects of electric current. (i) When current was allowed to pass through a wire AB placed along the axis of magnetic needle kept directly below and close to the wire that needle was found to deflect from its normal position. (ii) The deflection of the needle was found to be in the opposite direction on reversing the direction of the current by reversing the polarity of the battery.  (iii) Deflection of the magnetic needle change with the strength of the electric current. The deflection of the needle increase with the increase in current and vice versa  He concluded that an electric current (i.e. Flow of electric charges) in a conductor produce magnetic field in the space around the conductor. In another words flow of electric charges is the source of magnetic field. Ampere's swimming Rule :  Direction of the deflection of magnetic needle due to electric current in a conductor can be found by...

Magnetic field due to current carrying solenoid :  Consider a very long solenoid having n turns per unit length of solenoid.Let current I be flowing through the solenoid. The magnetic field inside the solenoid is almost uniform , strong and directed along. The axis of the solenoid. The magnetic field outside a very long solenoid is very weak and can be neglected.  Step 1 : Let P be a point well within the solenoid. Consider any rectangular loop ABCD ( known as Amperian Loop ) passing through P. Then  $\oint \overrightarrow{B}.\overrightarrow{dl}$ = Line integral of magnetic field across the loop ABCD,  $\oint \overrightarrow{B}.\overrightarrow{dl}= \int_{A}^{B} \overrightarrow{B}.\overrightarrow{dl} + \int_{B}^{C} \overrightarrow{B}.\overrightarrow{dl} + \int_{C}^{D} \overrightarrow{B}.\overrightarrow{dl} + \int_{D}^{A} \overrightarrow{B}.\overrightarrow{dl}$ $\overrightarrow{B}$ is perpendicular to paths BC and AD i.e. angle between $\overrightarrow{B}$ and $\overr...

Expression For Torque on current carrying rectangular loop placed in uniform magnetic field - Param Himalaya  Consider a rectangle conducting loop ABCD of a wire of length l and width b carrying current I ( clock wise ) is placed in a uniform magnetic field $\overrightarrow{B}$. The magnetic field $\overrightarrow{B}$ is acting X - axis along X-axis and the Normal of the plane of the loop $\hat{n}$ makes an angle $\theta$ with the magnetic field B.  The magnetic field B is perpendicular to the arms AB and CD of the loop and the angle between the arm BC or AD and the magnetic field is not 90°. Force acting on the arm AB of the conducting loop carrying current I due to magnetic field is given by :  $$\overrightarrow{F_{1}} = I(\overrightarrow{l}\times \overrightarrow{B})$$ According to Fleming's left hand rule , direction of $\overrightarrow{F_{1}}$ is perpendicular to the length of arm AB and directed into the plane of the paper  The magnitude of force $\overrightarro...

Sensitivity of a Galvanometer :  A galvanometer is said to be sensitive if a small current flowing through the coil of galvanometer produces a large deflection in the galvanometer.  (i) Current Sensitivity:  The current sensitivity of a Galvanometer is defined as the deflection produced in the coil of the galvanometer per unit current flowing through it. $$Current \ sensitivity = \frac{\phi}{I}$$ $$Current \ sensitivity = \frac{\phi}{\frac {k\phi}{NAB}}$$ $$Current \ sensitivity = \frac{\phi NAB}{k\phi}$$ $$Current \ sensitivity = \frac{NAB}{k}$$ Current sensitivity can be increased by :  (a) Increasing N  (b) Increasing B  (C) Increasing A (d) Decreasing k  (ii) Voltage sensitivity:  Voltage sensitivity of a Galvanometer is defined as the deflection produced in the coil of the galvanometer per unit voltage applied to it.  $$Voltage sensitivity= \frac{\phi}{V}$$ $$Voltage sensitivity= \frac{\phi}{IR}$$ $$Voltage\ sensitivity = \frac{\phi} {\...

Moving coil Galvanometer:  It is a device used to detect small current flowing in the electric circuit.  Principle :  Moving coil Galvanometer is based on the fact that when a current carrying loop or coil is placed in the uniform magnetic field , it experiences a torque. Construction:  it consists of a coil of copper wire wound on cylindrical soft iron core. The coil is pivoted in a uniform radial magnetic field provided by the concave shaped poles of a permanent magnet. The coil rotates freely about the pivot. A light pointer is attached to the coil. The pointer moves over a scale. A spring is attached to the coil to provide a restoring torque to the coil.  Theory :   Let B = Intensity of magnetic field  I = Current flowing through the coil L = length of coil b = Breadth of the coil N = Number of turns in the coil When current flows through the coil , it experiences a torque, which is given by : $$\tau = NIABsin \theta$$ Where , $\theta$ is the ...