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
B0.12 TI = ?30°L = 40 cm

A straight wire 40 cm long lies at 30° to a uniform magnetic field of 0.12 T. The magnetic force on it is 0.024 N. Find the current I.

B = 0.12 TF = 0.024 NL = 40 cmθ = 30°
I = A
2.Easy
B = 25.13 mTI = 4 AL = 20 cmN = ?

A solenoid 20 cm long carries 4 A. How many turns N must it have for a flux density of 25.13 mT inside?

I = 4 AL = 20 cmB = 25.13 mTμ₀ = 4π × 10⁻⁷ T·m/A
N =
3.Medium
nBA = 10 cm², N = 10B = 0.2 T

A coil of 10 turns has an area of 10 cm². The coil sits in a uniform field of 0.2 T perpendicular to its plane, and the field is switched off in 40 ms. Find the average induced emf ε.

N = 10A = 10 cm²B = 0.2 TΔt = 40 ms
ε = mV
4.Medium
R = 10 Ωv = 8 m/sL = 40 cmB = 0.8 T

A metal rod 40 cm long slides at 8 m/s along two rails in a uniform field of 0.8 T into the page. The rails are joined by a resistor of 10 Ω; the rod and rails have negligible resistance. Find the current I.

B = 0.8 TL = 40 cmv = 8 m/sR = 10 Ω
I = mA
5.Hard
Bn = ?12 cm × 20 cmN = 500B = 0.1 T

A coil of 500 turns, 12 cm × 20 cm, rotates in a uniform field of 0.1 T about an axis perpendicular to the field. At what speed n (in revolutions per minute) must it turn to give an rms emf of 79.97 V?

N = 500A = 12 cm × 20 cmB = 0.1 TErms = 79.97 V
n = rpm
6.Hard
E = 2 × 10⁴ V/m, B1​ = 0.25 TB2​ = 0.4 Tr = ?

A deuteron passes undeflected through a velocity selector with crossed fields E = 2 × 10⁴ V/m and B₁ = 0.25 T. It then enters a second region with only a magnetic field B₂ = 0.4 T, at right angles. Find the radius r of its path there.

E = 2 × 10⁴ V/mB1 = 0.25 TB2 = 0.4 Tm = 3.344 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C
r = cm

Answer key

  1. 1. I = 1 A
  2. 2. N = 999.9
  3. 3. ε = 50 mV
  4. 4. I = 256 mA
  5. 5. n = 900 rpm
  6. 6. r = 0.4175 cm

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