Q4. Assertion: the electric field of a charge does not depend on the test charge used to measure it. Reason: the force on the test charge is proportional to the test charge. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: since F ∝ q, the ratio F/q is the same whatever q is (NCERT page 15).
Q5. An electron is in a uniform field of 1.0 × 103 N C−1. Find the size and direction of its acceleration. Take e = 1.6 × 10−19 C and me = 9.11 × 10−31 kg.
a = eE/me = (1.6 × 10−19 × 1.0 × 103)/
Q6. Two charges of +4 µC each are 0.2 m apart. What is the field at the midpoint between them?
Zero. The two fields have the same size, 9 × 109 × 4 × 10−6/(0.1)2 = 3.6 × 106 N C−1, but point in opposite directions, away from each charge (NCERT Eq. (1.10), page 16).
Q7. Two point charges qA = 3 µC and qB = −3 µC are 20 cm apart in vacuum. (a) What is the field at the midpoint O of AB? (b) What force does a negative test charge of 1.5 × 10−9 C feel there? (NCERT Exercise 1.8, page 42)
(a) Each charge is 0.10 m from O and gives (9 × 109)(3 × 10−6)/(0.10)2 = 2.7 × 106 N C−1, both pointing from A towards B: E = 5.4 × 106 N C−1, along OB. (b) The force magnitude is F = |q|E = (1.5 × 10−9)(5.4 × 106) = 8.1 × 10−3 N, opposite to the field, so along OA, because the test charge is negative.
Q8. NCERT Figure 1.30 shows the tracks of three charged particles entering a uniform field between a positive upper plate and a negative lower plate. Particles 1 and 2 bend towards the positive plate, particle 3 towards the negative plate, and particle 3 bends the most. Give the signs of the charges. Assuming equal entry speeds perpendicular to the field, which particle has the greatest magnitude of charge-to-mass ratio? (NCERT Exercise 1.13, pages 42–43)
The field points from the positive plate to the negative one. Particles 1 and 2 are pushed against the field, so they are negative; particle 3 is pushed along it, so it is positive. Across the field each particle has acceleration qE/m, so after travelling a distance x at speed v it is deflected by y = qEx2/(2mv2). Taking the particles to enter with the same speed, the largest deflection at the same x means the largest |q|/m: particle 3 (compare NCERT Example 1.7, pages 17–18).