Final answer:
The magnitude of the magnetic induction in air at 10 cm from the center of a dipole on a line at a 30° angle from the axis of the dipole is not given among the options, but it is calculated to be 0.005 T.
Step-by-step explanation:
To calculate the magnetic induction (also referred to as the magnetic field B) at 10 cm from the center of a short dipole, making an angle of 30° from the axis of the dipole, we can use the formula for the magnetic field due to a dipole at a point in space:
B = µ0/(4π) * (m×/(r³)),
where µ0 is the magnetic constant (permeability of free space), m is the magnetic moment, θ is the angle from the axis of the dipole, and r is the distance from the dipole. Plugging in the values (µ0 = 4π × 10−7 N·A−2, m = 1 A·m², θ = 30°, r = 0.1 m), we get:
B = (4π × 10−7)/(4π) * (1 × sin(30°))/(0.1³) = 10−7 * (1/2) / (10−6)
B = 5 × 10−3 T or 0.005 T
Therefore, none of the given options (a. 1.0 T, b. 0.5 T, c. 0.866 T, d. 1.155 T) match the correct magnitude of the magnetic induction.