Qstnid -Iv-1-calculate The Dimensions Of (A) ∫E→.dl,→ (B) Vbl And (C) Dφbdt. The Symbols Have Their Usual Meaning. - 38: Electromagnetic Induction - Neet-xii-physics

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NEET-XII-Physics

38: Electromagnetic Induction

with Solutions - page 4

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#1
Calculate the dimensions of (a) ∫E→.dl,→ (b) vBl and (c) dΦBdt. The symbols have their usual meaning.
Ans : (a) The quantity`` \int ``E.dl can also be written as:
`` \int ``E.dl = V (V = Voltage)
Unit of voltage is J/C.
Voltage can be written as:
`` \,\mathrm{\,Voltage\,}=\frac{\,\mathrm{\,Energy\,}}{\,\mathrm{\,Charge\,}}``
Dimensions of energy = [ML²T^-2]
Dimensions of charge = [IT]
Thus, the dimensions of voltage can be written as:
[ML²T^-2] ×[IT]^-1 = [ML²I^-1T^-3] (b) The quantity vBl is the product of quantities v, B and L.
Dimensions of velocity v = [LT^-1]
Dimensions of length l = [L]
The dimensions of magnetic field B can be found using the following formula:
`` B=\frac{F}{qv}``
Dimensions of force F = [MLT^-2^]
Dimensions of charge q = [IT]
Dimensions of velocity = [LT^-1]
The dimensions of a magnetic field can be written as:
MI^-1T^-2
∴ Dimensions of vBl = [LT^-1] × [MI^-1T^-2] × [L]= [ML²I^-1T^-3] (c) The quantity `` \frac{d\,\mathrm{\,\varphi \,}}{dt}`` is equal to the emf induced; thus, its dimensions are the same as that of the voltage.
Voltage can be written as:
`` \,\mathrm{\,Voltage\,}=\frac{\,\mathrm{\,Energy\,}}{\,\mathrm{\,Charge\,}}``
Dimensions of energy = [ML²T^-2]
Dimensions of charge = [IT]
The dimensions of voltage can be written as:
[ML²T^-2] ×[IT]^-1 = [ML²I^-1T^-3]
∴ Dimensions of `` \frac{d\,\mathrm{\,\varphi \,}}{dt}`` = [ML²I^-1T^-3]
Page No 306:

#1-a
∫E→.dl,→
Ans : The quantity`` \int ``E.dl can also be written as:
`` \int ``E.dl = V (V = Voltage)
Unit of voltage is J/C.
Voltage can be written as:
`` \,\mathrm{\,Voltage\,}=\frac{\,\mathrm{\,Energy\,}}{\,\mathrm{\,Charge\,}}``
Dimensions of energy = [ML²T^-2]
Dimensions of charge = [IT]
Thus, the dimensions of voltage can be written as:
[ML²T^-2] ×[IT]^-1 = [ML²I^-1T^-3]

#1-b
vBl and
Ans : The quantity vBl is the product of quantities v, B and L.
Dimensions of velocity v = [LT^-1]
Dimensions of length l = [L]
The dimensions of magnetic field B can be found using the following formula:
`` B=\frac{F}{qv}``
Dimensions of force F = [MLT^-2^]
Dimensions of charge q = [IT]
Dimensions of velocity = [LT^-1]
The dimensions of a magnetic field can be written as:
MI^-1T^-2
∴ Dimensions of vBl = [LT^-1] × [MI^-1T^-2] × [L]= [ML²I^-1T^-3]

#1-c
dΦBdt. The symbols have their usual meaning.
Ans : The quantity `` \frac{d\,\mathrm{\,\varphi \,}}{dt}`` is equal to the emf induced; thus, its dimensions are the same as that of the voltage.
Voltage can be written as:
`` \,\mathrm{\,Voltage\,}=\frac{\,\mathrm{\,Energy\,}}{\,\mathrm{\,Charge\,}}``
Dimensions of energy = [ML²T^-2]
Dimensions of charge = [IT]
The dimensions of voltage can be written as:
[ML²T^-2] ×[IT]^-1 = [ML²I^-1T^-3]
∴ Dimensions of `` \frac{d\,\mathrm{\,\varphi \,}}{dt}`` = [ML²I^-1T^-3]
Page No 306: