8.4-1 Consider a magnetic field probe consisting of a flat circular loop of wire with radius 10 cm. The probe’s terminals correspond to a small gap in the loop. This probe is placed in a uniform magnetic field having magnitude B(t) = B0 sin(2πf t + α), where f = 100 kHz and α is an unknown constant. (By uniform, we mean that the magnetic field has the same magnitude and direction at all points in space.) The orientation of the loop with respect to the magnetic field vector is unknown. The voltage at the terminals is measured for all possible orientations of the probe, and it is found that the maximum voltage is 20 mV peakto-peak. What is B0?

B_o = 1.013μT

Explanation:

To find B_o you take into account the formula for the emf:

where you used that A (area of the loop) is constant, an also the angle between the direction of B and the normal to A.

By applying the derivative you obtain:

when the emf is maximum the angle between B and the normal to A is zero, that is, cosθ = 1 or -1. Furthermore the cos function is 1 or -1. Hence:

hence, B_o = 1.013μT

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: