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Q.1. A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre.     (2019)
A: Increases as r increases for both r < R and r > R
B: Zero as r increases for r < R, decreases as r increases for r > R
C: Zero as r increases for r < R, increases as r increases for r > R
D: Decreases as r increases for both r < R and r > R
Answer: B
Solution: Charge Q will be distributed over the surface of hollow metal sphere.
(i) For r < R (inside)
By Gauss law,
⇒ E_in = 0  (∵ q_en = 0)
(ii) For r > R (outside)




Q.2. Two parallel infinite line charges with linear charge densities +λ C/m and λl C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?     (2019)
A: Zero
B:
C:
D:
Answer: C
Solution:

Electric field due to line charge (1)

Electric field due to line charge (2)

Q.3. Two point charges A and B, having charges +Q and –Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes :     (2019)
A: F
B: 9F/16
C: 16F/9
D: 4F/3
Answer: B
Solution:

If 25% of charge of A transferred to B then



Q.4. An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electrical field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in through the same vertical distance h. The time fall of the electron, in comparison to the time fall of the proton is :-      (2018)
A: smaller
B: 5 times greater
C: 10 times greater
D: equal
Answer: A
Solution:

Q.5. A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric fieldDue to the forceits velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively :-    (2018)
A: 2 m/s, 4 m/s
B: 1 m/s, 3 m/s
C: 1 m/s, 3.5 m/s
D: 1.5 m/s, 3 m/s
Answer: B
Solution:
0 < t < 1s : velocity increases from 0 to 6 m/s
1 < t < 2s : velocity decreases from 6 to 0 m/s
but car continues to move forward
2 < t < 3s : since field strength is same ⇒ same acceleration
∴ car's velocity increases
from 0 to –6 m/s



Q.6. Two identical charged spheres suspended from a common point by two mass less strings of lengths ℓ are initially at a distance d(d << ℓ) a part because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as :    (2016)
A: v ∝ x^-1
B: v ∝ x^1/2
C: v ∝ x
D: v ∝ x^-1/2
Answer: D
Solution: