Test Index

NCERT Class XII Chapter
Electric Charges and Fields
Questions With Solutions

© examsnet.com
Question : 8 of 34
Marks: +1, -0
Two point charges qAq_A = 3 μC and qBq_B = –3 μC are located 20 cm apart in vacuum.
(a) What is the electric field at the midpoint O of the line AB joining the two charges?
(b) If a negative test charge of magnitude 1.5 × 10−910^{-9} C is placed at this point, what is the force experienced by the test charge?
Solution:  
(a) Electric fields at O due to the charges at A and B are
EOAE_{OA} = EOBE_{OB} = 14πε0qr2\frac{1}{4\pi\varepsilon_0}\frac{q}{r^2} = 9 × 10910^9 × 3×10−6 C(202×10−2 m)2\frac{3\times10^{-6}\,\mathrm{C}}{\left(\frac{20}{2}\times10^{-2}\,\mathrm{m}\right)^2}
or EOAE_{OA} = EOBE_{OB} = 27 × 10510^5 N C−1\mathrm{N}\,\mathrm{C}^{-1}
As, they are directed in same direction, so net electric field at midpoint O is
E = EOAE_{OA} + EOBE_{OB} = 2EOB2E_{OB} = 2 × 27 × 10510^5
or E = 5.4 × 106 N C−110^6\,\mathrm{N}\,\mathrm{C}^{-1} directed along OB.
(b) When test charge q0q_0 = - 1.5 × 10−910^{-9} C is placed at point O, it experiences a force
F = q0Eq_0E = 1.5 × 10−910^{-9} × 5.4 × 10610^6 or F = 8.1 × 10−310^{-3} N
In direction opposite to that of E i.e. along OA.
© examsnet.com
Go to Question:
Prev Question
Next Question