Inductive charging is used to wirelessly charge electronic devices ranging from toothbrushes to cell phones. Suppose the base unit of an inductive charger produces a 1.50 ✕ 10−3 T magnetic field. Varying this magnetic field magnitude changes the flux through a 16.0-turn circular loop in the device, creating an emf that charges its battery. Suppose the loop area is 2.75 ✕ 10−4 m2 and the induced emf has an average magnitude of 5.30 V. Calculate the time required (in s) for the magnetic field to decrease to zero from its maximum value.

Explanation:

Given :

Magnetic field

No. of turns

Area of loop

Average emf  

From the faraday's electromagnetic induction principle,

Average emf

Where change in magnetic flux, change in time.

The magnetic flux is given by,

In our example, we have to find time required to decrease magnetic field so our above equation is modified as,

for decrease in magnetic field.

Where time required for the magnetic field to decrease to zero from its maximum value

        sec.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft