A magnetic field `B = B_(0) (y//a)(hat)k` is into the paper in the +z direction, `B_(0)` and a are

A charged particle of specific charge (charge/mass) alpha released from origin at time t=0 with velocity vec v = v_0 (hat i + hat j) in uniform magnetic field vec B = B_0 hat i. Coordinates of the particle at time t= pi//(B_0 alpha) are

A magnetic field vec(B) = B_(0)hat(j) , exists in the region a ltxlt2a , and vec(B) = -B_(0) hat(j) , in the region 2a lt xlt 3a , where B_(0) is a positive constant . A positive point charge moving with a velocity vec(v) = v_(0) hat (i) , where v_(0) is a positive constant , enters the magnetic field at x= a . The trajectory of the charge in this region can be like

A loop made of straight edegs has six corners at A(0,0,0), B(L, O,0) C(L,L,0), D(0,L,0) E(0,L,L) and F(0,0,L) . Where L is in meter. A magnetic field B = B_(0)(hat(i) + hat(k))T is present in the region. The flux passing through the loop ABCDEFA (in that order) is

A conductor AB of length l moves in x y plane with velocity vec(v) = v_(0)(hat(i)-hat(j)) . A magnetic field vec(B) = B_(0) (hat(i) + hat(j)) exists in the region. The induced emf is

In a region at a distance r from z-axis, magnetic field vec(B) = B_(0)rt hat(k) is present where B_(0) is constant and t is time. Then the magnetic of induced electric field at a distance r from z-axis is given by

In region x gt 0 a uniform and constant magnetic field vec(B)_(1) = 2 B_(0) hat(k) exists. Another uniform and constant magnetic field vec(B)_(2) = B_(0) hat(k) exists in region x lt 0 A positively charged particle of mass m and charge q is crossing origin at time t =0 with a velocity bar(u) = u_(0) hat(i) . The particle comes back to its initial position after a time : ( B_(0),u_(0) are positive constants)