1
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is :
A
$${1 \over {4\pi {\varepsilon _0}}}{{\left( {R + r} \right)} \over {\left( {{R^2} + {r^2}} \right)}}$$Q
B
$${1 \over {4\pi {\varepsilon _0}}}{{\left( {R + r} \right)} \over {2\left( {{R^2} + {r^2}} \right)}}Q$$
C
$${1 \over {4\pi {\varepsilon _0}}}{{\left( {R + 2r} \right)Q} \over {2\left( {{R^2} + {r^2}} \right)}}$$
D
$${1 \over {4\pi {\varepsilon _0}}}{{\left( {2R + r} \right)} \over {\left( {{R^2} + {r^2}} \right)}}Q$$
2
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
A charged particle (mass m and charge q)
moves along X-axis with velocity V0. When it
passes through the origin it enters a region having uniform electric field
$$\overrightarrow E = - E\widehat j$$ which extends upto x = d.
Equation of path of electron in the region x > d is
A
y = $${{qEd} \over {mV_0^2}}\left( {x - d} \right)$$
B
y = $${{qEd} \over {mV_0^2}}\left( {{d \over 2} - x} \right)$$
C
y = $${{qEd} \over {mV_0^2}}x$$
D
y = $${{qE{d^2}} \over {mV_0^2}}x$$
3
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
Consider a sphere of radius R which carries a uniform charge density $$\rho$$. If a sphere of radius $${{R \over 2}}$$ is carved out of it, as shown, the ratio $${{\left| {\overrightarrow {{E_A}} } \right|} \over {\left| {\overrightarrow {{E_B}} } \right|}}$$ of magnitude of electric field $${\overrightarrow {{E_A}} }$$ and $${\overrightarrow {{E_B}} }$$, respectively, at points A and B due to the remaining portion is :
A
$${{17} \over {54}}$$
B
$${{18} \over {54}}$$
C
$${{18} \over {34}}$$
D
$${{21} \over {34}}$$
4
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
An electric dipole of moment
$$\overrightarrow p = \left( { - \widehat i - 3\widehat j + 2\widehat k} \right) \times {10^{ - 29}}$$ C.m is
at the origin (0, 0, 0). The electric field due to this dipole at
$$\overrightarrow r = + \widehat i + 3\widehat j + 5\widehat k$$ (note that $$\overrightarrow r .\overrightarrow p = 0$$ ) is parallel to :
A
$$\left( { + \widehat i + 3\widehat j - 2\widehat k} \right)$$
B
$$\left( { + \widehat i - 3\widehat j - 2\widehat k} \right)$$
C
$$\left( { - \widehat i + 3\widehat j - 2\widehat k} \right)$$
D
$$\left( { - \widehat i - 3\widehat j + 2\widehat k} \right)$$
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