The component of the force in negative z-direction is -0.144 N.
The given parameters;
- <em>current in the wire, I = 2.7 A</em>
- <em>length of the wire, L = (3.2 i + 4.3j) cm</em>
- <em>magnetic filed, B = 1.24 i</em>
The force on the segment of the wire is calculated as follows;

where;
- <em>θ is the angle wire and magnetic field</em>
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The force on the wire segment will be perpendicular in negative z-direction (applying right hand rule), so there won't be any x and y component of the force.
The angle between the wire and the magnetic field is calculated as follows;

The magnitude of the wire length is calculated as follows;

The component of the force in negative z-direction is calculated as;

Thus, the component of the force in negative z-direction is -0.144 N.
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Using Fleming’s left hand rule,
The magnetic force on the electron will be west. Example: If it is dropped above the equator in Africa, the electron will head towards North America.
Get a pull chord light switch installed in her bathroom by a qualified electrician asap. Meanwhile, keep hands as dry as possible, and try not to go near that switch until it's either been properly earthed, or whatever the problem actually is, and get qualified advice on what the problem is. Don't have wet feet either, and don't stand in puddles of water whilst operating - i she has to - the switch. 250V AC mains can be lethal, and at least painful.