A uniform conducting wire of length 18a and resistance R is wound up as current carrying coil in the shape of a regular a hexagon of sides a. If the coil is connected to a voltage source `V_(0)`, then the magnetic moment of coil is

Options

A. `6sqrt3(V_(0))/(R)a^(2)A m^(2)`
B. `(9sqrt3)/(2) (V_(0)a^(2))/(R)A m^(2)`
C. `(7sqrt3)/(2) (V_(0)a^(2))/(R)A m^(2)`
D. `(11sqrt3)/(2) (V_(0)a^(2))/(R)A m^(2)`

Answer

B

Explanation

In the regular hexagon, if each arm length is a, then the number of turns in the given shape, `n=(18a)/(6a)=3`
Now the area of given shape is
`A=(3sqrt3a^(2))/(2)`
Now magnetic moment `M = nIA`
`=3xxIxx(3sqrt3)/(2)a^(2)=(9sqrt3)/(2)(V_(o)a^(2))/(R) "A m"^(2)" "("where "I=(V_(o))/(R))`