Electricity and Magnetism – Page 4

Physics concepts and problems for the JEE

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:

Rendered by QuickLaTeX.com

$|\Delta \phi| = \frac{1}{2} B_0 v_0 L$ 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.

Insulating spherical shell with a hole

December 30th, 2021jeefirst0 Comments

JEE Advanced 2019 Paper 1, Question 2.

A thin spherical insulating shell of radius $R$ carries a uniformly distributed charge such that the potential at its surface is $V_0$ . A hole with a small area $\alpha 4 \pi R^2 \ (\alpha \ll 1)$ is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

The potential at the center of the shell is reduced by $2 \alpha V_0$
The magnitude of the eletric field at the center of the shell is reduced by $\frac{\alpha V_0}{2 R}$
The ratio of the potential at the center of the shell to that of the point at $R/2$ from center towards

…