Electric Potential & Energy
Q-Define electric potential at a point. Is it a scalar or a vector quantity?
A-The electric potential (V) at any point in an electric field is defined as the amount of work done (W) per unit positive test charge (q) in bringing it from infinity to that point against the electrostatic forces.
V=W/q
It is a scalar quantity. Unit of V is joule/coulomb or Volt.
Q-State two properties of an equipotential surface.
A- (1)No work is done in moving a test charge between two points on an equipotential surface
(2)Electric field lines are always perpendicular to the equipotential surface at every point.
Q-Derive the relationship between electric field intensity (E) and electric potential (V).
A- Watch my video solution. click below.
Q-Can two equipotential surfaces intersect each other? Justify your answer
A-No, two equipotential surfaces can never intersect each other.
If they were to intersect, there would be two different values of electric potential at the point of intersection. Consequently, there would be two different directions for the electric field at that single point, which is physically impossible.
Q-Deduce an expression for the potential energy of a system of two point charges q1and q2 separated by a distance r.
A- Watch video solution. click below.
Q-Define the term ‘potential energy’ of charge ‘q’ at a distance r in an external electric field.
A-It is defined as the amount of work done in bringing the charge from infinity to its position in the system in the electric field of another charge without acceleration.
W=q.V
Q-A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. What is the potential at the centre of the sphere?
A-The electric field inside the shell is zero. This implies that potential is constant inside the shell (as no work is done in moving a charge inside the shell) and, therefore, equals its value at the surface, which is 10 V.
Q-What is the geometrical shape of equipotential surfaces due to a single isolated charge?
A-Concentric spheres with a gap between them not being uniform as V ∝1/r
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Q-“For any charge configuration, equipotential surface through a point is normal to the electric field.” Justify.
A-Work done in moving a charge over an equipotential surface is zero, hence a point on it will be normal to the electric field.
W = FS cos θ ∴ cos θ = 0 or θ = 90 degrees.
Q-What is the formula of electric potential energy for a system of two charge q1 and q2 , differ by distance r?
A- U=k.q1q2/r
Q-Is it possible , that electric potential at a point be zero, while electric field at that point is not zero.
A- yes , it is possible .due to an electric dipole at any point on perpendicular bisector electric field is not zero but electric potential is always zero.
Q-Does the charge given to a metallic sphere also depends on weather it is solid or hollow?
A- No. given charge to a metal sphere always distributed on its surface , it not depends on it is solid or hollow. for same potential amount charge will be same , sphere is solid or hollow not an issue .