A thick hollow cylinder of height h and inner and outer radii a and b(b>a) made up of a poorly conducting material of resistivity lies coaxially inside a long solenoid at its middle. The radius of the solenoid is larger

Olympiad workbook

Exam: Olympiad workbook
Subject: NSEP
Chapter: Electromagnetic Induction

Olympiad workbook · NSEP · Electromagnetic Induction

A thick hollow cylinder of height h and inner and outer radii a and...

A thick hollow cylinder of height

h

and inner and outer radii

a

and

b(b>a)

made up of

a

poorly conducting material of resistivity

\rho

lies coaxially inside a long solenoid at its middle. The radius of the solenoid is larger than b. Throughout the interior of the solenoid, a uniform time varying magnetic field

B=\beta t

is produced parallel to solenoid axis. Here

\beta

is a constant. In this time varying magnetic field

Options

Athe emf induced at a certain radius $\mathrm{r}(\mathrm{a} < \mathrm{r} < \mathrm{b})$ in the hollow cylinder is $\pi r^2 \beta$
Bthe induced current circulating in the thick hollow cylinder between radii a and b is $i=\frac{\beta h}{4 \rho} \left(b²-a²\right)
Cthe resistance offered to the circulation of current by the thick hollow cylinder is $R=\frac{2 \pi \rho}{h \times \ln \frac{b}{a}}$
Dno electric field is detectable outside the solenoid.

Correct answer

C. the resistance offered to the circulation of current by the thick hollow cylinder is $R=\frac{2 \pi \rho}{h \times \ln \frac{b}{a}}$

Step-by-step solution

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