Charges kept in uniform magnetic field:
Let's say we have switched on a uniform magnetic field of 1.5 Tesla.
However, it would not exert any force on -12C charge. This is because the magnetic fields exert force only on moving / flowing charges.
It would mean that each stationary charged particle kept in this magnetic field would experience a zero force.
However, consider if the charged particle kept in a uniform magnetic field (say 1.5 Tesla) is given some velocity, then it starts experiencing a force. This force is specifically called Lorentz force ($F_B$).
Let's say we gave a constant velocity of 1 m/s to the charge -12 C. Since, this is velocity we will also take direction in account, to calculate the force. Let's consider the charge is moving at an angle of $90\degree$ (perpendicular) with the uniform magnetic field.
Now, 1 Tesla of uniform magnetic field technically means that a charged particle of unit magnitude (i.e. 1 C) moving inside the magnetic field with a uniform speed of 1 m/s making an angle of 90° with the magnetic field, then the force exerted on that charged particle will be 1 Newtons !!
For lorentz force, the relation is given as : $\mathrm{\text{F = q }(\overrightarrow{v} \times \overrightarrow{B})}$
$$\mathrm{\text{F = q v B sin}\theta}$$
$\text{Putting values, we get}$
$$\mathrm{\text{F = }-12\times 1 \times 1.5 \times \text{sin}90\degree \text{ N} }$$
$$\mathrm{\text{F = }-12\times 1 \times \frac{3}{2} \times 1} \text{ N}$$
$$\mathrm{\text{F = }- \overset{6}{\cancel{12}} \times \frac{3}{\cancel{2}} \text{ N}}$$
$$\mathrm{ \text{F = }-18\text{ N}}$$ {Negative sign just means that the direction will be opposite to the direction given by Fleming's left hand rule}
We can find the direction of magnetic force as well by using the fleming left hand rule. But since we took negative charge, we need to reverse the direction we got by this way. This is because fleming left hand rule is designed to get the direction of lorentz force of moving postive charges. For negative charges, either reverse the direction that you got by your left hand, or use the right hand instead. Let's see how.. /refer next post/
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