A person drives a car around a circular road with a constant speed of 20 m/s. The
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Question is missing. Found on internet the complete text of the problem:
"<span>Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surface charge density of −9.70µC/m2, and sheet B, which is to the right or A, carries a uniform charge density of −11.5 µC/m2. Assume the sheets are large enough to be treated as infinite. Find the magnitude and direction of the net electric field these sheets produce at a point (a) 4.00 cm to the right of sheet A; (b) 4.00 cm to the left of sheet A; (c) 4.00 cm to the right of sheet B."
Solution:
(a) The electric field produced by a uniformly charged sheet at any distance is given by
</span>
where
is the charge density and 
is the vacuum permittivity.
First of all, let's compute the fields generated by the two sheets separately. The two densities of charge are
and 
.
Sheet a gives an electric field of
where the negative sign means the field points towards sheet A, in any point of the space.
The electric field produced by sheet B is given by:
and again, the negative sign means that the field at any point of the space points towards sheet B.
The point at which we have to compute the total field is at 4.00 cm right of sheet A. Since the two sheets are 5.00cm far apart, it means that this point is between the two sheets. Therefore, in this point the two fields point into opposite directions. Therefore, the total field is
And the direction is towards sheet B, since it has a field with stronger intensity.
(b) Field at 4.00 cm to the left of sheet A: in this point of the space, the two fields point towards same direction (on the right, towards both sheet A and sheet B). So, the total field is simply the sum of the two fields:
towards right.
(c) Field at 4.00 cm to the right of sheet B. As before, the two fields in this point have same direction (both towards left, pointing towards both sheet A and sheet B). And so, the total field is simply the sum of the two fields:
towards left.
"<span>Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surface charge density of −9.70µC/m2, and sheet B, which is to the right or A, carries a uniform charge density of −11.5 µC/m2. Assume the sheets are large enough to be treated as infinite. Find the magnitude and direction of the net electric field these sheets produce at a point (a) 4.00 cm to the right of sheet A; (b) 4.00 cm to the left of sheet A; (c) 4.00 cm to the right of sheet B."
Solution:
(a) The electric field produced by a uniformly charged sheet at any distance is given by
</span>
where
First of all, let's compute the fields generated by the two sheets separately. The two densities of charge are
Sheet a gives an electric field of
where the negative sign means the field points towards sheet A, in any point of the space.
The electric field produced by sheet B is given by:
and again, the negative sign means that the field at any point of the space points towards sheet B.
The point at which we have to compute the total field is at 4.00 cm right of sheet A. Since the two sheets are 5.00cm far apart, it means that this point is between the two sheets. Therefore, in this point the two fields point into opposite directions. Therefore, the total field is
And the direction is towards sheet B, since it has a field with stronger intensity.
(b) Field at 4.00 cm to the left of sheet A: in this point of the space, the two fields point towards same direction (on the right, towards both sheet A and sheet B). So, the total field is simply the sum of the two fields:
towards right.
(c) Field at 4.00 cm to the right of sheet B. As before, the two fields in this point have same direction (both towards left, pointing towards both sheet A and sheet B). And so, the total field is simply the sum of the two fields:
towards left.
Answer:
emf = 0.02525 V
induced current with a counterclockwise direction
Explanation:
The emf is given by the following formula:
(1)
ФB: magnetic flux = BA
B: magnitude of the magnetic field = 1.00T
A2: final area of the loop; A1: initial area
t2: final time, t1: initial time
You first calculate the final A2, by taking into account that the circumference of loop decreases at 11.0cm/s.
In t = 4 s the final circumference will be:
To find the areas A1 and A2 you calculate the radius:
r1 = 0.261 m
r2 = 0.190 m
Then, the areas A1 and A2 are:
Finally, the emf induced, by using the equation (1), is:
The induced current has counterclockwise direction, because the induced magneitc field generated by the induced current must be opposite to the constant magnetic field B.