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Properties of Field Lines

Three points ...

Question

Three points A, B and C are shown for different systems of charge configuration. A charge +Q is uniformly distributed in I, II and III but a point charge +Q is involved in IV. E represents electric field, V represents electric potential. $(K = \frac{1}{4 π ε_{0}} a n d R = R a d i u s i n e a c h c a s e)$

Which of the following options is the correct combination for point C?

A

I (iv) S

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B

III (iv) Q

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C

IV (ii) P

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D

IV (iv) R

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Solution

The correct option is D IV (iv) R
$\begin{matrix} r < R & r < R F o r S o l i d n o n - c o n d u c t i n g s p h e r e & E = \frac{K Q r}{R^{3}} & E = \frac{K Q}{r^{2}} V = \frac{K Q}{2 R} (3 - \frac{r^{2}}{R^{2}}) & V = \frac{K Q}{r} \end{matrix}$

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Similar questions

Q. Physical quantities in Column 1 are represented in the form of dimensional formulae (Column 2) and some derived formulae(Column 3) (where P

\to

\to

potential difference, m

\to

\to

electric field, J

\to

current density, h

\to

Planck’s constant , C

\to

speed of light,

λ \to

ε_{0} \to

permittivity of vacuum, Q

\to

\begin{matrix} C o l u m n 1 & C o l u m n 2 & C o l u m n 3 (I) & L a t e n t H e a t & (i) & M L^{- 1} T^{- 2} & (P) & \frac{P^{2}}{m V^{2}} (I I) & C a p a c i t a n c e & (i i) & L^{2} T^{- 2} & (Q) & \frac{E}{J} (I I I) & E n e r g y d e n s i t y & (i i i) & M L^{3} t^{- 1} Q^{- 2} & (R) & ε_{0} R^{2} (I V) & R e s i s t i v i t y & (i v) & M^{- 1} L^{- 2} T^{2} Q^{2} & (S) & \frac{h C}{λ m} \end{matrix}

Which one of the following combination is correct ?

Q. A non conducting sphere of radius

^{'} a^{'}

has a type charge

^{'} + q^{'}

uniformly distributed throughout in volume. A hollow spherical conductor having inner and outer, radii

^{'} b^{'}

^{'} c^{'}

^{'} - q^{'}

is concentric with the sphere (see the figure)
Read the following statements
(i) The electric field at a distance

r

from the center of the sphere

= \frac{1}{4 π ε_{0}} \frac{q r}{a^{3}}

r < a

.
(ii) The electric field at distance

r

from the center of the sphere for

a < r < b = 0

(iii) The electric field at distance

r

from the center of the sphere for

b < r < c <= 0

(iv) The charge on the inner surface of the hollow sphere

= - q

(v) The charge on the outer surface of the hollow sphere

= + q

.

Q. Observe the circuit in the figure and match the following (assume

q_{1}, q_{2},

q_{3}

to be the charges on the three capacitors

C_{1}, C_{2}

C_{3}

Column I Column II

i.	$q_{1} (in μ C)$	p.	50
ii.	$q_{2} (in μ C)$	q.	10/3
iii.	$q_{3} (in μ C)$	r.	140/3
iv.	Potential difference across the 6 $μ F$ capacitor is (in V)	s.	25/3

Q. Two infinite sheets having charge densities

σ_{1}

σ_{2}

are placed in two perpendicular planes whose two-dimensional view is shown in Fig. The charges are distributed uniformly on the sheet in electrostatic equilibrium condition. Four points are marked I, II, III, and IV. The electric field intensities at these points are

{\to E}_{1}, {\to E}_{2}, {\to E}_{3}, a n d {\to E}_{4}

, respectively. The correct expression for the electric field intensities is :

A charged particle is projected with velocity $\to v = u^i$ from the origin, in a region having electric field $\to E$ and magnetic field $\to B$ both. Value of $\to B$ and $\to E$ are given in column 1 and column 2 respectively and path of the particle is given in column 3.

$\begin{matrix} Column 1 & Column 2 & Column 3 (Magnetic field) & (Electric field) & (Path of particle) (i) & \to B = 0 & (i) & \to E = 0 & (P) & Circular path (i i) & \to B = B_{0}^i + B_{0}^j & (i i) & \to E = E_{0}^i & (Q) & Helical path (i i i) & \to B = B_{0}^j + B_{0}^k & (i i i) & \to E = B_{0} u (^j -^k) & (R) & Cycloid (i v) & \to B = B_{0}^k & (i v) & \to E = E_{0}^k & (S) & Straight line \end{matrix}$

In which of the following combination particle moves in uniform circular motion?

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