Magnetic fields & induction worksheet with answers

Free printable Magnetic fields & induction worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A solenoid 25 cm long carries 4 A. How many turns N must it have for a flux density of 16.08 mT inside?

I = 4 AL = 25 cmB = 16.08 mTμ₀ = 4π × 10⁻⁷ T·m/A

N =

2.Easy

A solenoid 10 cm long carries 5 A. How many turns N must it have for a flux density of 125.7 mT inside?

I = 5 AL = 10 cmB = 125.7 mTμ₀ = 4π × 10⁻⁷ T·m/A

N =

3.Medium

A metal rod 60 cm long slides at 2 m/s along two rails in a uniform field of 0.25 T into the page. The rails are joined by a resistor of 5 Ω; the rod and rails have negligible resistance. Find the current I.

B = 0.25 TL = 60 cmv = 2 m/sR = 5 Ω

I = mA

4.Medium

A coil of 20 turns has an area of 200 cm². A uniform field perpendicular to the coil rises steadily from 0.2 T to 1 T in 40 ms. Find the average induced emf ε.

N = 20A = 200 cm²B: 0.2 T → 1 TΔt = 40 ms

ε = V

5.Hard

A coil of 250 turns, 15 cm × 20 cm, rotates at 3000 rpm in a uniform field of 0.4 T about an axis perpendicular to the field. Find the rms value E_rms of the emf.

N = 250A = 15 cm × 20 cmB = 0.4 Tn = 3000 rpm

E_rms = V

6.Hard

A proton starts from rest, is accelerated through a potential difference of 1000 V and then enters a uniform magnetic field of 0.4 T at right angles. Find the radius r of its path in the field.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CV = 1000 VB = 0.4 T

r = cm

Answer key

1. N = 799.8
2. N = 2001
3. I = 60 mA
4. ε = 8 V
5. E_rms = 666.4 V
6. r = 1.143 cm

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