In a region of space , suppose there exists a uniform electric field `vec(E ) = 10 hat(i) ( V /m)` . If a positive charge moves with a velocity `vec(v ) = -2 hat(j)`, its potential energy

The potential field of an electric field vec(E)=(y hat(i)+x hat(j)) is

The potential field of an electric field vec(E)=(y hat(i)+x hat(j)) is

The potential field of an electric field vec(E)=(y hat(i)+x hat(j)) is

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 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

In a certain region static electric and magentic fields exist. The magnetic field is given by vec(B) = B_(0) (hat(i) + 2hat(j)-4hat(k)) . If a test charge moving with a velocity, vec(upsilon) = upsilon_(0)(3hat(i)-hat(j) +2hat(k)) experience no force in that region, then the electric field in the region, in SI units, is-

In a certain region static electric and magentic fields exist. The magnetic field is given by vec(B) = B_(0) (hat(i) + 2hat(j)-4hat(k)) . If a test charge moving with a velocity, vec(upsilon) = upsilon_(0)(3hat(i)-hat(j) +2hat(k)) experience no force in that region, then the electric field in the region, in SI units, is-

In a certain region static electric and magentic fields exist. The magnetic field is given by vec(B) = B_(0) (hat(i) + 2hat(j)-4hat(k)) . If a test charge moving with a velocity, vec(upsilon) = upsilon_(0)(3hat(i)-hat(j) +2hat(k)) experience no force in that region, then the electric field in the region, in SI units, is-

An electron of charge -e , mass m, enters a uniform magnetic field vec(B)= B hat(i) with an initial velocity vec(v) = v_(x) hat(i) + v_(y) hat(j) . What is the velocity of the electron after a time interval of t seconds?

A particle ( mass = m and charge = q ) is moving in a region in which there exists a uniform electric field E vec( i ) and a uniform magnetic field B hat (k) . At t = 0 , the particle is at ( 0,a ) and is moving with v hat(i) . After some time, the particle is located at ( 2a, 0 ) and has a velocity - 2 v hat( j ) , then which of the following is true ?