1. The magnitude of the magnetic field doubles
Explanation: the intensity of the magnetic field produced by a current-carrying wire is given by:
[tex]I=\frac{\mu_0 I}{2 \pi r}[/tex]
where [tex]\mu_0[/tex] is the vacuum permeability, I is the current in the wire, r is the distance from the wire.
As we see from the formula, the intensity of the magnetic field is directly proportional to the current: if the current increases from 5 A to 10 A, it means it doubles, so the magnetic field doubles as well.
2. The magnitude of the magnetic field halves
Explanation: the intensity of the magnetic field produced by a current-carrying wire is given by:
[tex]I=\frac{\mu_0 I}{2 \pi r}[/tex]
We see that the magnitude of the magnetic field is inversely proportional to the distance from the wire (r). In this case, the distance of the particle is changed from 10 cm to 20 cm, so it is doubled: therefore, the magnitude of the field will become half of the initial value.
3. The force reverses direction
Explanation: the force exerted on a charged particle in a magnetic field is:
[tex]F=qvB sin \theta[/tex]
where q is the charge, v is the speed of the particle, B is the magnetic field intensity and [tex]\theta[/tex] the angle between the direction of v and B. If the charge of the particle is switched from 2 µC to –2µC, the magnitude of the force does not change (because the absolute value of q does not change), however the charge q gets a negative sign (-), so the sign of the force changes and gets a negative sign too, so the force reverses direction.
(a) When the current increases from 5 A to 10 A, the strength of the magnetic field increases.
(b) When the distance from the wire increases, the strength of the magnetic field decreases.
(c) When the sign of the charge changes and the magnitude is the same, the strength of the magnetic force will remain the same.
The magnetic field due to a distance from a wire is given as follows;
[tex]B = \frac{\mu_o I}{2\pi r}[/tex]
where;
Thus, when the current increases from 5 A to 10 A, the strength of the magnetic field increases.
Also, when the distance from the wire increases, the strength of the magnetic field decreases.
The magnetic force on a charged particle moving in a magnetic field is given as;
F = qvB
where;
The magnetic force considers the magnitude of the charge, thus when the sign of the charge changes and the magnitude is the same, the strength of the magnetic force will remain the same.
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