A Radiometer Has Two Square Vanes $( 1.0 \mathrm {~cm}$ By $1.0 \mathrm {~cm} )$

Multiple Choice

A radiometer has two square vanes $( 1.0 \mathrm {~cm}$ by $1.0 \mathrm {~cm} )$ , attached to a light horizontal cross arm, and pivoted about a vertical axis through the center, as shown in the figure. The center of each vane is $6.0 \mathrm {~cm}$ from the axis. One vane is silvered and it reflects all radiant energy incident upon it. The other vane is blackened and it absorbs all incident radiant energy. Radiant energy, having an intensity of $300 \mathrm {~W} / \mathrm { m } ^ { 2 }$ , is incident normally upon the front of both vanes. What is the net torque on the vane assembly, about the vertical axis? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } , \varepsilon _ { 0 } = 8.85 \times \right.$ $10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 }$ )

A) $0.0 \mathrm {~N} \cdot \mathrm { m }$
B) $1.2 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m }$
C) $1.8 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m }$
D) $2.4 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m }$
E) $6.0 \times 10 ^ { - 12 } \mathrm {~N} \cdot \mathrm { m }$