A solid sphere of radius R has total charge Q. The charge is distributed in spherically symmetric manner in the sphere. The charge density is zero at the centre and increases linearly with distance from the centre. (a) Find the charge density at distance r from the centre of the sphere. (b) Find the magnitude of electric field at a point ‘P’ inside the sphere at distance `r_1` from the centre.
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Let A and B two symmetric matrices of order 3. Statement 1 : `A(BA)` and `(AB)A` are symmetric matrices. Statement 2 : `AB` is symmetric matrix if mat
Correct Answer - C `(A(BA))^(T)=(BA)^(T) A^(T)` `=(A^(T) B^(T)).A^(T)` `=(AB) A` `=A(BA)` Similarly `((AB)A)^(T)=(AB)A` Clearly both statements are true but statement 2 is not a correct explanation of statement 1.
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A solid non conducting sphere of radius R and uniform volume charge density `rho` has its centre at origin. Find out electric field intensity in vecto
(i) At `(R//2, 0, 0)` : Distance of point from centre `=sqrt((R//2)^(2)+0^(2)+0^(2))=R//2 lt R`, so point lies inside the sphere, so `vec(E)=(p vec(r))/(3 epsi_(0))=rho/(3 epsi_(0)) [R/2 hat(i)]` (ii) At `(R/sqrt(2),...
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A uniformly charged sphere has charge Q. An electron (charge – e, mass m) revolves around it in a circular orbit of radius r. (a) Write the total ener
Correct Answer - (a). `-(Qe)/(8pi in_(0)r)` (b). 8T
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A conducting sphere of radius R carries a charge Q. It is enclosed by another concentric spherical shell of radius 2R. Charge from the inner sphere is
Correct Answer - `-(Q^(2))/(16pi in_(0)R)`
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A ball of radius R has a uniformly distributed charge Q. The surrounding space of the ball is filled with a volume charge density `rho=(b)/(r)` , wher
Correct Answer - (a). `Q=2pibR^(2)` (b). `E=(b)/(2epsilon_(0))`
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Electric charge +q is iniformaly distributed over the entire volume of a sphere of radius r. Calculate the magnetic moment of the sphere if it spins a
Correct Answer - `(1)/(5)qwr^(2),(q)/(2m)`
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An insulated sphere of radius 10 cm has a positive charge of 20 nC and another of radius 5 cm has a positive charge of 15 nC. If the two are connected
Correct Answer - A charge of `3.33muC` will flow from 5-cm sphere to 10-cm sphere, 2100V,
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A spherical shell of radius `R_(1)` with uniformly distributed charge q has a point charge `q_(0)` at its centre. Find the work performed by the elect
Correct Answer - `(q(q_(0)+q//2))/(4piepsilon_(0))((1)/(R_(1))-(1)/(R_(2)))`
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Consider three identical metal spheres ` A, B` and `C`. Sphere `A` carries charge ` + 6q`, sphere `B` carries charge `-3q` and sphere `C` carries no c
Correct Answer - `2.25q`
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A non-conducting sphere ofradius R has a positive charge which is distributed over its volume with density `rho= rho_(0)(1- (x)/(R))` per unit volume,
Correct Answer - `[(pirho_(0)^(2)R^(5))/(72 in_(0)) , (13pirho_(0)^(2)R^(5))/(630 in_(0))]`
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