A magnet of magnetic moment 50i Am2 is placed . . .

Question : A magnet of magnetic moment 50i Am² is placed along the x-axis in a magnetic field B=(0.5i+3j) T. The torque acting on the magnet is :

a) 175 k Nm

b) 150 k Nm

c) 75 k Nm

d) 25√37 k Nm

Doubt by Angad

Solution : 

m=50i Am²

B=(0.5i+3j) T

We know, 

𝛕 = m×B

𝛕 = 50i×(0.5i+3j)
𝛕 = 50i×(0.5i+3j)

𝛕 = 25(i×i)+150(i×j)
𝛕 = 25(0)+150(k) [∵i×i = 0, i×j=k]
𝛕 =150(k)

𝛕 =150k Nm

Hence, b) 150 k Nm would be the correct option.