Q1 of 104 Page 306

Calculate the dimension of

(a) (b) vBℓ (c)


The symbols have their usual meanings.



(a)using faraday’s law of induction



Where ϵ is the emf or voltage


has thus the dimensions of voltage


Voltage is given by formula



Where


W=work done


Q=charge


Dimensions of W=


Dimensions of Q=


The dimensions of voltage can be given as



……(i)


(b) vBl is the motional emf developed due to motion of conductor of length l with velocity v in a magnetic field (B)


Therefore, vBl has same dimensions as of voltage


Therefore, by eqn.(i)



(c) by faraday’s law of electromagnetic induction



Where


ϵ =emf produced


ϕ =flux of magnetic field


thus has same dimensions as of emf or voltage


therefore, by eqn.(i)



Therefore , and all have same dimensional formula equal to


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(a) The magnetic field in a region varies as shown in figure. Calculate the average induce emf in a conducting loop of area 2.0 × 10–3 m2 placed perpendicular to the field in each of the 10 ms intervals shown.

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