Question

In a demonstration, a 4.00 cm2 square coil with 10 000 turns enters a larger square region with a uniform 1.50 T magnetic field at a speed of 100 m/s. The plane of the coil is perpendicular to the field lines. If the breakdown voltage of air is 4 000 V/cm on that day, the largest gap you can have between the two wires connected to the ends of the coil and still get a spark is:

Answer 1

Step-by-step explanation:

It is given that,

Area of square coil,
`A=4\ cm^2=0.0004\ m^2`

Side of the square, L = 0.02 m

Number of turns, N = 10000

Uniform magnetic field, B = 1.5 T

Speed, v = 100 m/s

An emf is induced in the coil which is given by :

`E=NBLv`

`E=10000* 1.5* 0.02* 100`

E = 30000 V

Breakdown voltage of air,
`V=4000\ V/cm=400000\ V/m`

Let d is the gap between the two wires connected to the ends of the coil and still get a spark. So,

Electric field,
`E'=(V)/(d)`

`(30000)/(d)=400000`

d = 0.075 m

Hence, this is the required solution.