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Answer:
The ratio of electric field is 16:9.
Explanation:
Given that,
Radius
Charge = Q
We know that,
The electric field is directly proportional to the charge and inversely proportional to the square of the distance.
In mathematically term,
Here,
We need to calculate the ratio of electric field
Using formula of electric field
Put the value into the formula
Hence, The ratio of electric field is 16:9.
(a) , -k direction
First of all, let's find the magnetic field produced by the wire at the location of the electron:
where
I = 19.0 A is the current in the wire
r = 1.9 cm = 0.019 m is the distance of the electron from the wire
Substituting,
and the direction is +j direction (tangent to a circle around the wire)
Now we can find the force on the electron by using:
where
is the electron's charge
is the electron speed
is the magnetic field
is the angle between the direction of v and B
In this case, the electron is travelling away from the wire, while the magnetic field lines (B) form circular paths around the wire: this means that v and B are perpendicular, so . So, the force on the electron is
The direction is given by the right hand rule:
- Index finger: direction of motion of the electron, +i direction (away from the wire)
- Middle finger: direction of magnetic field, +j direction (tangent to a circle around the wire)
- Thumb: direction of the force --> since the charge is negative, the sign must be reversed, so it means -k direction (anti-parallel to the current in the wire)
(b) , +i direction
The calculation of the magnetic field and of the force on the electron are exactly identical as before. The only thing that changes this time is the direction of the force. In fact we have:
- Index finger: direction of motion of the electron, +k direction (parallel to the current in the wire)
- Middle finger: direction of magnetic field, +j direction (tangent to a circle around the wire)
- Thumb: direction of the force --> since the charge is negative, the sign must be reversed, so it means +i direction (away from the wire)
(c) 0
In this case, the electron is moving tangent to a circle around the wire, in the +j direction. But this is exactly the same direction of the magnetic field: this means that v and B are parallel, so , therefore the force on the electron is zero.