First slide

Applications involving charged particles moving in a magnetic field

Question

A coil in the shape of an equilateral triangle of side 0.02 m is suspended from a vertex such that it is hanging in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field of $5 \times 10^{- 2} T$ . Find the couple acting on the coil when a current 0.1 A is passed through it (the magnetic field is parallel to its plane).

Moderate

A

$8.66 \times 10^{- 7} N m$
B

$86.6 \times 10^{7} N m$
C

$86.6 \times 10^{- 17} N m$
D

$8.66 \times 10^{17} N m$

Solution

The couple acting on a closed loop is given by $τ = N i A B \sin θ$
Where, N=number of loops, A=area of loop, B=magnetic field and $θ$ =angle between
magnetic field and normal to the surface of the loop.
Here, $N = 1, i = 0.1 A, B = 5 \times 10^{- 2} T, θ = 90^{0}$ (the magnetic field is parallel to its plane)
And $A = \frac{\sqrt{3}}{4} a^{2} = \frac{\sqrt{3}}{4} {(0.02)}^{2}$ $= 1.732 \times 10^{- 4} m^{2}$

$τ = N i A B \sin θ$
$∴ τ = 1 \times 0.1 \times (1.732 \times 10^{- 4}) \times (5 \times 10^{- 2}) \times 1$ $= 8.66 \times 10^{- 7} N m$ .

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