The current in a long solenoid of radius 5 cm and 17 turns/cm is varied with time at a rate of 5 A/s. A circular loop of wire of radius 7 cm and resistance 5 Ω surrounds the solenoid. Find the electrical current induced in the loop (in µA).

The current is  

Explanation:

From the question we are told that

   The first radius is

    The number of turns is

    The current rate is  

    The second radius is  

     The resistance is

Generally the magnetic flux induced in the solenoid is mathematically represented as

 Where  is the magnetic field mathematically represented as

Where is the permeability of free space with a value of

     and A is the area mathematically represented as

So

            Substituting values

The induced emf is mathematically represented as

substituting values

From Ohm law

Substituting values

A picture frame will have the same gravitational potential energy as the book when it’s raised to a height of 1.4 m.

Explanation:

Given that,

Weight of book = 0.35 kg

Height of shelf = 2.0 m

Weight of frame = 0.5 kg

Using formula of gravitational potential energy

Gravitational potential energy = mgh

Where, m = mass

g = acceleration due to gravity

h = height

A picture frame that weighs 0.5 kilograms will have the same gravitational potential energy as the book when it’s raised to a height.

Therefore,

Gravitational potential energy of book = gravitational potential energy of frame

mgh=m'gh'

We substitute the value into equation (I)

Hence, A picture frame will have the same gravitational potential energy as the book when it’s raised to a height of 1.4 m.