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Chapter 4: Q39E (page 984)

A long, thin solenoid has 400 turns per meter and radius 1.10 cm. The current in the solenoid is increasing at a uniform rate di/dt. The induced electric field at a point near the centre of the solenoid and 3.50 cm from its axis is 8.00 x 10-6 V/m. Calculate di/dt

Short Answer

Expert verified

If a long thin solenoid having 400 turns per meter and radius of , the current in the solenoid is increasing at a unform rate of 9.21A/s

Step by step solution

01

Calculating the value of E

It is given that a long solenoid of 400 turns and distance of m-1and a radius of 1.10cm . The induced electric field at a point near the centre of the solenoid is 3.50cm and induced electric field is 8.00脳10-6V/m

Now using Faraday鈥檚 law we get:

蔚=鈭�E鈫�.dl鈫�=-d蠒Bdt

Now, the magnetic flux through the circle of radius r > R :

蠒=AB=蟺搁2B

Now integrating LHS we get:

鈭�E鈫�.dl鈫�=E2蟺r

Absolute value of E is:

E2蟺r=蟺R2dBdt

We can also write it as:

E=R2渭0n2r=dBdt

02

Calculating the values

Now to get dldtwe get:

dldt=2Er渭0nR2

Now, substituting the values we get:

28.00脳10-6V/m0.0350m4蟺脳10-7T.m/A4000.0110m2=9.21A/s

Therefore, the value ofdldt is = 9.21A/s

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