A particle of mass m and charge q is released from rest in a region with uniform electric field E and uniform magnetic field B, both directed along the positive z-axis. Which of the following statements is true about the motion of the particle?

The particle will move in a straight line along the z-axis.

The particle will move in a helical path.

The particle will move in a circular path in the xy-plane.

The particle will remain at rest.

Two identical conducting spheres, A and B, are initially far apart. Sphere A has a charge of +Q and sphere B has a charge of -Q. They are then brought into contact and subsequently separated. What is the final charge on each sphere?

Sphere A has charge 0, Sphere B has charge 0.

Sphere A has charge +Q, Sphere B has charge -Q.

Sphere A has charge +Q/2, Sphere B has charge -Q/2.

Sphere A has charge +Q, Sphere B has charge 0.

The electric flux remains unchanged.

The electric flux becomes half.

The electric flux becomes zero.

The potential difference doubles.

The potential difference becomes half.

The potential difference remains unchanged.

The potential difference becomes four times.

The fringe width decreases by approximately 9.1%.

The fringe width increases by 10%.

The fringe width remains unchanged.

The fringe width increases by approximately 9.1%.

-A * omega^2 * cos(omega*t + phi)

A * omega^2 * cos(omega*t + phi)

-A * omega * sin(omega*t + phi)

IIT Jee Advanced physics problems - Test Paper