QJEEM07Ph6896: JEE Main 2007 Physics - Class 12 JEEM07Ph6896 Solution: An electric charge is placed at the origin of co-ordinate…

Question

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An electric charge

{10^{ - 3}}\,\,\mu \,C

is placed at the origin

(0,0)

of

X-Y

co-ordinate system. Two points

A

and

B

are situated at

\left( {\sqrt 2 ,\sqrt 2 } \right)

and

\left( {2,0} \right)

respectively. The potential difference between the points

A

and

B

will be

Accepted Answer

The distance of point

A\left( {\sqrt 2 ,\sqrt 2 } \right)

from the origin,

OA = \left| {\overrightarrow {{r_1}} } \right|

= \sqrt {{{\left( {\sqrt 2 } \right)}^2} + {{\left( {\sqrt 2 } \right)}^2}}

= \sqrt 4 = 2

The distance of point

B(2,0)

from the origin,

OB = \left| {\overrightarrow {{r_2}} } \right| = \sqrt {{{\left( 2 \right)}^2} + {{\left( 0 \right)}^2}} = 2

units.

Now, potential at

A,

{V_A} = {1 \over {4\pi { \in _0}}}.{Q \over {\left( {OA} \right)}}

Potential at

B,

{V_B} = {1 \over {4\pi { \in _0}}}.{Q \over {\left( {Ob} \right)}}

\therefore

Potential difference between the points

A

and

B

is zero.

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