Electric Charges And Fields

Q: An electric line of force in the xy-plane is given by equation x^{2} + y^{2} = 1 . A particle with unit positive charge, initially at rest at the point x = 1, y = 0 in the xy - plane .

Charge will move along the circular line of force because x^{2} + y^{2} = 1 is the equation of circle in xy - plane .

Q: Two identical charged spheres suspended from a common distance d(d < < 1) apart because of their mutual repulsion. The charged begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v . Then v varies as a function of the distance x between the spheres, as

From figure \tan \theta = \dfrac {F_{e}}{mg} =\theta \dfrac {kq^{2}}{x^{2}mg} = \dfrac {x}{2l} or x^{3}\propto q^{2} .... (1) or x^{3/2} \propto q ..... (2) Differentiating eq. (1) w.r.t time 3x^{2} \dfrac {dx}{dt}\propto 2q \dfrac {dq}{dt} but \dfrac {dq}{dt} is constantso x^{2}(v) \propto q Replace q from eq. (2) x^{2}(v) \propto x^{3/2} or v\propto x^{-1/2} .

Question

An electric line of force in the $x y - p l a n e$ is given by equation $x^{2} + y^{2} = 1$ . A particle with unit positive charge, initially at rest at the point $x = 1, y = 0$ in the $x y - p l a n e$ .

Electric Charges And Fields

Physics 307 Views

An electric line of force in the xy−plane is given by equation x2+y2=1. A particle with unit positive charge, initially at rest at the point x=1,y=0 in the xy−plane.

Physics
307 Views

An electric line of force in the $x y - p l a n e$ is given by equation $x^{2} + y^{2} = 1$ . A particle with unit positive charge, initially at rest at the point $x = 1, y = 0$ in the $x y - p l a n e$ .