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  1. Problems
  2. /A solenoid has 600 turns in a length of 0.25 m and carries 1.5 A…
MediumPhysicsHigh School (9–10)Electricity & Magnetism › Magnetic Effects of CurrentNumerical

A solenoid has 600 turns in a length of 0.25 m and carries 1.5 A…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A solenoid has 600600600 turns in a length of 0.25 m0.25\ \text{m}0.25 m and carries 1.5 A1.5\ \text{A}1.5 A. Take μ0=4π×10−7 T m/A\mu_0 = 4\pi \times 10^{-7}\ \text{T m/A}μ0​=4π×10−7 T m/A.

  1. How many turns are there in each metre?
  2. What is the field inside?
  3. The coil is stretched to 0.5 m0.5\ \text{m}0.5 m, with the same turns and current. What is the field now?

Check your answer

Work it out on paper, then type your number. The answer itself stays hidden.

mT
mT
Need a reminder? The key ideaShowHide

Inside a long solenoid the field is strong and uniform: B=μ0 n IB = \mu_0\,n\,IB=μ0​nI, where nnn is the number of turns in each metre and μ0=4π×10−7 T m/A\mu_0 = 4\pi \times 10^{-7}\ \text{T m/A}μ0​=4π×10−7 T m/A. A soft iron core makes it an electromagnet, many times stronger, that loses its magnetism when the current stops.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. Turns in each metre. n=6000.25 m=2400n = \dfrac{600}{0.25\ \text{m}} = 2400n=0.25 m600​=2400 turns per metre.

Step 2. The field. B=4π×10−7 T m/A×2400 m−1×1.5 A=4.52×10−3 T=4.52 mTB = 4\pi \times 10^{-7}\ \text{T m/A} \times 2400\ \text{m}^{-1} \times 1.5\ \text{A} = 4.52 \times 10^{-3}\ \text{T} = 4.52\ \text{mT}B=4π×10−7 T m/A×2400 m−1×1.5 A=4.52×10−3 T=4.52 mT.

Step 3. Stretched. n=6000.5 m=1200n = \dfrac{600}{0.5\ \text{m}} = 1200n=0.5 m600​=1200 turns per metre, half as many, so B=2.26 mTB = 2.26\ \text{mT}B=2.26 mT.

Answer: 240024002400 turns per metre, 4.52 mT4.52\ \text{mT}4.52 mT, and 2.26 mT2.26\ \text{mT}2.26 mT when stretched.

Check. 4.52 mT4.52\ \text{mT}4.52 mT is about 909090 times the Earth's field of 0.05 mT0.05\ \text{mT}0.05 mT.

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