Electric Potential - Class 12 PDF Download

 Page 1


1 
Page 2


1 2 
Two electric charge q and 2q are placed at a distance 6 
m apart on a horizontal plane. Find the locus of point on 
this plane where the potential has a value zero. 
Page 3


1 2 
Two electric charge q and 2q are placed at a distance 6 
m apart on a horizontal plane. Find the locus of point on 
this plane where the potential has a value zero. 
3 
If the point P is at a distance r
1
 from point 
charge (+q) and r
2
 from charge (-2q) 
??
??
??
? ? ? ?
??
??
12
0 1 2
12
4
P
qq
V V V
rr
According to given problem, V
P
 = 0 , i.e.,  
??
12
2
0
qq
rr
?
21
2 ...( ) r r ii
Solution 
Page 4


1 2 
Two electric charge q and 2q are placed at a distance 6 
m apart on a horizontal plane. Find the locus of point on 
this plane where the potential has a value zero. 
3 
If the point P is at a distance r
1
 from point 
charge (+q) and r
2
 from charge (-2q) 
??
??
??
? ? ? ?
??
??
12
0 1 2
12
4
P
qq
V V V
rr
According to given problem, V
P
 = 0 , i.e.,  
??
12
2
0
qq
rr
?
21
2 ...( ) r r ii
Solution 
4 
But if the charge q is assumed to be situated at the 
origin  
? ?
? ? ? ? ?
2
2 2 2 2 2
12
6 r x y and r x y
So, substituting these values of r
1
 and r
2
 in equation (i), 
we get  
? ?
? ? ?
2
2
2 16 xy
So the locus of the point P is a circle with radius 4 m 
and centre (-2, 0). 
Page 5


1 2 
Two electric charge q and 2q are placed at a distance 6 
m apart on a horizontal plane. Find the locus of point on 
this plane where the potential has a value zero. 
3 
If the point P is at a distance r
1
 from point 
charge (+q) and r
2
 from charge (-2q) 
??
??
??
? ? ? ?
??
??
12
0 1 2
12
4
P
qq
V V V
rr
According to given problem, V
P
 = 0 , i.e.,  
??
12
2
0
qq
rr
?
21
2 ...( ) r r ii
Solution 
4 
But if the charge q is assumed to be situated at the 
origin  
? ?
? ? ? ? ?
2
2 2 2 2 2
12
6 r x y and r x y
So, substituting these values of r
1
 and r
2
 in equation (i), 
we get  
? ?
? ? ?
2
2
2 16 xy
So the locus of the point P is a circle with radius 4 m 
and centre (-2, 0). 
5 
Two fixed charges -2Q and Q are located at the points 
with coordinates (-3a,0) and (+3a,0) respectively in the 
x-y plane.  
(a) Show that all points in the x-y plane where the 
electric potential due to the two charges is zero lie on a 
circle. Find its radius and the location of its centre. 
(b) Give the expression V (x) at a general  point  on 
the x-axis and sketch the function V (x) on the whole x-
axis. 
(c) If a particle of charge +q starts form rest at the 
centre of the circle, show by a short quantitative 
argument that the particle eventually crosses the circle. 
Find its speed when it does so