Trick – Page 3 – JEE First

Physics concepts and problems for the JEE

Electric field from a sphere with a cavity

January 8th, 2022jeefirst0 Comments

A sphere of radius $a$ is filled with positive charge with uniform density $\rho$ . Then a smaller sphere of radius $a/2$ is carved out, as shown in the figure below, and left empty. What are the direction and magnitude of the electric field at $A$ ? At $B$ ?

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Solution

This problem can be solved by using the principle of superposition. For instance, consider a point charge $+q$ at some point $P$ in space. It creates an electric field everywhere. However, if you place a …

Conducting wire in a magnetic field

December 30th, 2021jeefirst0 Comments

JEE Advanced 2019 Paper 1, Question 6

A conducting wire of parabolic shape, initially $y = x^2$ , is moving with velocity $\vec v = v_0 \hat i$ in a non-uniform magnetic field $\vec B = B_0 \left( 1 + \left( \frac{y}{L} \right)^\beta \right) \hat k$ , as shown in the figure below. If $v_0, B_0, L$ and $\beta$ are positive constants and $\Delta \phi$ is the potential difference developed between the ends of the wire, then the correct statement(s) is/are:

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$|\Delta \phi| = \frac{1}{2} B_0 v_0 L$ for $\beta = 0$ .
$|\Delta \phi| = \frac{4}{3} B_0 v_0 L$ for $\beta = 2$ .
$|\Delta \phi|$ remains the same if the parabolic wire is replaced by a straight wire, $y=x$ initially, of length $\sqrt{2} L$ .
$|\Delta \phi|$ is proportional to the length of the wire projected on the $y$ axis.