What is the result of an electric charge in uniform motion?

The dots in the figure depict a magnetic field that is perpendicular to the plane of the paper and emanates from it. The trajectory of a particle in the plane of the paper is depicted by the curve \(ABC\). What exactly is the particle?

A particle of charge \(+q\) and mass \(m\) moving under the influence of a uniform electric field \(E\hat i\) and a uniform magnetic field \(\mathrm B\hat k\) follows a trajectory from \(P\) to \(Q\) as shown in the figure. The velocities at \(P\) and \(Q\) are \(v\hat i\) and \(-2v\hat j\) respectively. Which of the following statement(s) is/are correct?

When a positively charged particle moves in an \(x\text-y\) plane, its path abruptly changes due to the presence of electric and/or magnetic fields beyond \(P\). The curved path is depicted in the \(x\text-y\) plane and is discovered to be noncircular. Which of the following combinations is true?
          
1. \(\vec{{E}}=0 ; \vec{{B}}={b} \hat{i}+{c} \hat{k}\) 
2. \(\vec{E}={a\hat{i}} ; \vec{B}={c} \hat{k}+a\hat{i}\)
3. \(\vec{E}=0 ; \vec{B}=c \hat{j}+b \hat{k}\)
4. \(\vec{E}=a\hat i ; \vec{B}=c\hat{k}+{b}\hat{j}\)

A charged particle is projected through a region in a gravity-free space. If it passes through the region with constant speed, then the region may have:
1. \(\vec{E}=0, \vec{B} \neq 0\)
2. \(\vec{E} \neq 0, \vec{B} \neq 0\)
3. \(\vec{E} \neq 0, \vec{B}=0\)
4. Both (1) & (2)

A current-carrying wire is placed in a uniform magnetic field in the shape of the curve \(y= \alpha \sin \left({\pi x \over L}\right),~0 \le x \le2L.\) $$
What will be the force acting on the wire?
                   

A current \(I\) is carried by an elastic circular wire of length \(L\). It is placed in a uniform magnetic field \(B\) (out of paper) with its plane perpendicular to \(B'\text{s}\) direction. What will happen to the wire?