Question

A wheel having mass m has charge +q and -q on diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of vertical electric field E. The value of E is__.
Ans: mg/2q

Answer 1

Answer on Question #75621, Physics / Electromagnetism

Question A wheel having mass m has charge +q and -q on diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of vertical electric field E. The value of E is .

Ans: mg/2q

Solution We can consider this wheel as dipole

$p=qd$

where $d$ is diameter of the wheel. The torque create by field is

$\tau=\vec{p}\times E=pE\sin\alpha=qdE\sin\alpha$

where $\alpha$ is angle of inclination of the plane. It is written for point where wheel touches the plane. We can also compute torque of the gravitational force:

$\tau_{g}=F\times r=mg\cdot d/2\cdot\sin\alpha$

Here we assumed that gravitational force is applied to the center of the wheel. Wheel is balanced, hence these torques are equal, from this we obtain

$\tau=\tau_{g}$

$qdE\sin\alpha=mg\cdot d/2\cdot\sin\alpha$

$E=\frac{mg}{2q}$