# Why isn't any current induced in a rectangular loop when it is moved in a uniform magnetic field with constant velocity?

It is said that the magnetic flux passing through the coil remains constant. But when the rectangular loop is moved out of field with constant velocity,then the magnetic flux decreases. Thus current is induced in that case. Why is the two case different?

• Can you clarify the geometry you're talking about? I'm guessing you mean the plane of the coil is at right angles to the field lines. May 27 '15 at 6:17
• Yeah the plane is at right angle. But why does the flux changes when it is moved out of field?
– Rima
May 27 '15 at 6:23
• I'm guessing that moving out of the field means moving sideways i.e. in the plane of the coil. Think about how many field lines per second are being intersected by the coil when moving (1) along a line normal to the plane of the coil and (2) along a line in the plane of the coil. May 27 '15 at 6:27
• So if the plane was moving out of the field at same position as while moving in(i.e at right angles) then there would be no any induced emf?
– Rima
May 27 '15 at 6:30
• Actually, now I think about it, there would be an EMF when moving out of the field even when moving normal to the plane of the coil. When you're moving in a uniform field the field strength is constant so $dB/dt = 0$. However when moving out of the field the field strength is changing so $dB/dt \ne 0$. That's the difference. May 27 '15 at 6:33

Why isn't any current induced in a rectangular loop when it is moved in a uniform magnetic field.

Because, there is no change to the flux passing through the loop. Suppose we're looking at a diagram of a 3cm tall rectangle on a page and the uniform field is into the page (it won't matter how wide the rectangle is for this explanation). Now, if you slide the rectangle, say, 1cm to the right, you win 3cm^2 of field on the right side but you lose 3cm^2 of field on the left side, and these cancel out (because the field is uniform).

But when the rectangular loop is moved out of field with constant velocity,then the magnetic flux decreases.

Yes, but then you haven't moved the rectangle within a uniform magnetic field. Uniform means it has the same value everywhere. Of course, there can't be any such thing as a truly "uniform" magnetic field. Yet, some regions of magnetic fields (such as the interior of a solenoid, or between the poles of a C-magnet) are well approximated by a uniform magnetic field. Which says nothing about the current that may be induced in a coil that leaves those regions of space (or rotates within those regions, which is another way to change the flux passing through it).

• But if it is still inside the uniform magnetic field but has started to move out. Then what happens?
– Rima
May 27 '15 at 7:23
• If the motion of the coil is entirely within the uniform magnetic field, and the angle of the coil with respect to the field remains the same, it doesn't matter how it moves; there won't be an induced current. May 27 '15 at 7:24
• Atsby, it would be good if you could make this quantitative by writing the equations for the induced EMF. May 27 '15 at 7:33
• @dream_girl17 I realized another way to interpret your follow-up question is what happens if a coil initially fully within a uniform magnetic field starts to move outside its "boundary". First of all, no real magnetic field will have a sharp boundary like that. But, considering such a field hypothetically, a current would be induced as soon as part of it starts to move outside the magnetic field. May 27 '15 at 8:50
• @atsby yeah if there is change in magnetic field then current will surely be induced but if it hasn't crossed its boundary then there won't b any induced current,right?
– Rima
May 27 '15 at 8:53

The definition of magnitude of induced emf(which produces induced current) is,

$|e| = \frac{d\phi}{dt}\space$ that is the induced emf in magnitude is equal to change in magnetic flux (say of a coil), also,

$\phi = BAcos\theta\space$

Hence the flux through the coil is changed when there is change in either Magnetic Field, $B$, The area of the coil inside the magnetic field, and the angle between the area vector(perpendicular to the plane of area) and the Magnetic field vector.

Answering your first question, There is no current induced because there is no change in any of the factors that contribute to change in flux (Magnetic Field, Area of the coil in the magnetic field and the angle between A and B, all remains constant).

In your second question the coil is moved out of the field, so that the area which is inside the magnetic field decreases and hence the magnetic flux decreases. Hence an emf is induced and current is also induced in the coil.