A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of loop is 1 cm s^–1 in a direction normal to the (i) longer side (ii) shorter side of the loop? For how long does the induced voltage last in each case?

Solution

Given,
Length of loop, l = 8 cm = 8 x 10^–2 m
Breadth of loop, b = 2 cm = 2 x 10^–2 m
Strength of magnetic field, B = 0.3 T
Velocity of loop, v = 1 cm/sec = 10^–2 m/sec

Let the field be perpendicular to the plane of the paper directed inwards.

(i)Then, the magnitude of induced emf is,
$ε = B . l . v$
$= 0.3 \times 8 \times 10^{- 2} \times 10^{- 2} = 2.4 \times 10^{- 4} V$

Time for which induced e.m.f. will last is equal to the time taken by the coil to move outside the field
$t = \frac{distance travelled}{velcoity} = \frac{2 \times 10^{- 2}}{10^{- 2} m} = 2 \sec .$

(ii) The conductor is moving outside the field normal to the shorter side.
b = 2 x 10^–2 m

∴ The magnitude of induced emf is
$ε = B . b . ν$
$= 0.3 \times 2 \times 10^{- 2} \times 10^{- 2} = 0.6 \times 10^{- 4} V$

Time, $t = \frac{distance}{velocity} = \frac{8 \times 10^{- 2}}{10^{- 2}} = 8 \sec .$

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Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

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