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  • A conducting loop of resistance R and radius r has its center at the origin of the co-ordinate system in a magnetic field of induction B axis. When it is rotated about Y-axis through 90° ,net c

A conducting loop of resistance R and radius r has its center at the origin of the co-ordinate system in a magnetic field of induction B axis. When it is rotated about Y-axis through 90° ,net charge flown in the coil is directly proportional to

Option: 1

\mathrm{1 / B}


Option: 2

R


Option: 3

\mathrm{r^2}


Option: 4

r


Answers (1)

best_answer

Induced emf in the loop when the variation of flux  \mathrm{(\mathrm{d} \phi)} during time dt is given as

\mathrm{\begin{aligned} & E=\frac{d \phi}{d t} \\ & \Rightarrow \quad \int_{\phi_1}^{\phi_2} \mathrm{~d} \phi=\Delta \phi=\int E d t ......(1) \end{aligned}}             

\mathrm{\Rightarrow \quad \text { The total charge flown in the loop }=q=\int i d t}

\mathrm{q=\int \frac{E}{R} d t}                                                           ...[2]

Using (1) and (2)

\mathrm{q=\frac{\Delta \phi}{R}}

where  \Delta \phi= change in flux given as \mathrm{\Delta \phi=\phi_2-\phi_1=\mathrm{B} \cdot\left(\pi \mathrm{r}^2\right)} because initially no flux is linked with the coil and it has maximum flux linkage \mathrm{\phi_2=\mathrm{B} \pi \mathrm{r}^2} when turned through 90°.

\mathrm{\begin{array}{cc} \Rightarrow \quad q & \quad=\frac{\pi B r^2}{R} \\ \Rightarrow \text { i.e. } & q \propto B \\ & q \propto r^2 \\ & q \propto(1 / R) . \end{array}}

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Gunjita

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