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  • A person wants to roll a solid non-conducting spherical ball of mass m and radius r on a surface whose coefficient of static friction is <img alt="\mu" src="https://entrancecorner.oncodecogs.com/gi

A person wants to roll a solid non-conducting spherical ball of mass m and radius r on a surface whose coefficient of static friction is \mu. He placed the ball on the surface wrapped with n turns of closely packed conducting coils of negligible mass at the diameter. By some arrangement he is able to pass a current i through the coils either in the clockwise direction or in the anti-clockwise direction.

A constant horizontal magnetic field B is present throughout the space as shown in the figure. (Assume \vec{B}is large enough to help rolling motion)

Question

If current i is passed through the coils the maximum torque in the coil is

 

Option: 1

\mathrm{-\pi \operatorname{nir}^2 B \hat{k}}


Option: 2

\mathrm{\pi \operatorname{nir}^2 \mathrm{~B} \hat{j}}


Option: 3

\mathrm{-\pi \operatorname{nir}^2 \mathrm{~B} \hat{j}}


Option: 4

\mathrm{\pi n i^2 \mathrm{~B} \hat{k}}


Answers (1)

best_answer

\mathrm{\begin{aligned} & \mathrm{\tau} =\vec{\mu} \times \overrightarrow{\mathrm{B}} \\ & =n i\left(\pi \mathrm{r}^2\right) \hat{\mathrm{j}} \times \mathrm{B} \hat{\mathrm{i}}=-\pi \operatorname{nir}^2 \mathrm{~B} \hat{\mathrm{k}} \end{aligned}}

Posted by

Pankaj Sanodiya

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