First slide

Magnetic dipole in a uniform magnetic field

Question

The torque required to keep a magnet of length 20 cm at 30º to a uniform field is 2×10^–5N-m. The magnetic force on each pole is

Moderate

A

2 × 10^–4 N
B

4 × 10^–4 N
C

2 × 10^–3 N
D

2 × 10^–6 N

Solution

$\begin{array}{rcl} τ & = & r x F = 2 l \sin θF; \\ F & = & \frac{τ}{2 l sinθ} \\ F & = & \frac{2 x 10^{- 5}}{20 x 10^{- 2} x \frac{1}{2}} = \frac{4 x 10^{- 5}}{20 x 10^{- 2}} = 2 x 10^{- 4} N \end{array}$

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